The Geometry of Curves in Projective Space via Degeneration and Deformation

通过退化和变形研究射影空间中的曲线几何

基本信息

  • 批准号:
    2200641
  • 负责人:
  • 金额:
    $ 22.48万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Standard Grant
  • 财政年份:
    2022
  • 资助国家:
    美国
  • 起止时间:
    2022-08-01 至 2025-07-31
  • 项目状态:
    未结题

项目摘要

Systems of polynomial equations are ubiquitous in mathematics, and related fields such as physics, cryptography, and other sciences. When such a system describes a one-dimensional object, the corresponding geometric object is known as an algebraic curve. Broadly speaking, this project studies the geometry of algebraic curves, both individually and as they vary in families. One specific question this project investigates is the concept of interpolation: When can a certain type of curve be passed through a general collection of points? In other words, one can draw a line through any two points in the plane and draw a circle through any three points in the plane, unless those three points lie on a line. More generally, the PI will consider what happens for other types of curves in higher-dimensional spaces, assuming again that the points do not lie in any special configurations. This project also includes training for undergraduate students. The project considers various questions for the investigation of the structure of the equations of general curves. For example, in what degrees are they generated? What is the Betti table of a general divisor on such a curve? The PI will also investigate certain natural vector bundles on curves that control their deformation theory --- the restricted tangent bundle and the normal bundle --- and study how they break down into stable vector bundles, which are the atomic building blocks of all vector bundles. Finally, the PI will study the geometry of moduli spaces of curves, focusing on their integral intersection theory.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
多项式方程组在数学以及相关领域如物理学、密码学和其他科学中无处不在。当这样的系统描述一维对象时,对应的几何对象被称为代数曲线。从广义上讲,这个项目研究代数曲线的几何,无论是单独的,因为他们在家庭中的变化。这个项目研究的一个具体问题是插值的概念:什么时候某种类型的曲线可以通过一般的点集?换句话说,人们可以通过平面上的任意两点画一条线,并通过平面上的任意三点画一个圆,除非这三点位于一条线上。更一般地说,PI将考虑高维空间中其他类型的曲线会发生什么,再次假设这些点不位于任何特殊的配置中。该项目还包括对本科生的培训。该项目考虑了各种问题的一般曲线方程的结构的调查。 例如,它们是在什么程度上产生的?在这样一条曲线上的通约数的贝蒂表是什么?PI还将研究控制其变形理论的曲线上的某些自然向量束-限制切束和法束-并研究它们如何分解为稳定的向量束,这些向量束是所有向量束的原子构建块。最后,PI将研究曲线模空间的几何学,重点是它们的积分相交理论。该奖项反映了NSF的法定使命,并通过使用基金会的知识价值和更广泛的影响审查标准进行评估,被认为值得支持。

项目成果

期刊论文数量(3)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Stability of Tschirnhausen Bundles
Tschirnhausen 丛的稳定性
Constructing reducible Brill–Noether curves II
构建可简化的布里尔-诺特曲线 II
  • DOI:
    10.1007/s00229-022-01408-9
  • 发表时间:
    2022
  • 期刊:
  • 影响因子:
    0.6
  • 作者:
    Larson, Eric
  • 通讯作者:
    Larson, Eric
Constructing Reducible Brill--Noether Curves
构建可简化的布里奇--诺特曲线
  • DOI:
  • 发表时间:
    2022
  • 期刊:
  • 影响因子:
    0.9
  • 作者:
    Larson, Eric
  • 通讯作者:
    Larson, Eric
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Eric Larson其他文献

The embedding theorem in Hurwitz-Brill-Noether Theory
Hurwitz-Brill-Noether 理论中的嵌入定理
  • DOI:
  • 发表时间:
    2023
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Kaelin Cook;D. Jensen;Eric Larson;H. Larson;Isabel Vogt
  • 通讯作者:
    Isabel Vogt
Making the Case for Continuous Learning from Routinely Collected Data
从定期收集的数据中持续学习的理由
  • DOI:
    10.31478/201304d
  • 发表时间:
    2012
  • 期刊:
  • 影响因子:
    3.7
  • 作者:
    S. Okun;PatientsLikeMe;D. McGraw;P. Stang;Eric Larson;D. Goldmann;J. Kupersmith;R. Filart;R. Robertson;Claudia Grossman;Michael D. Murray
  • 通讯作者:
    Michael D. Murray
Cuestiones relativas al personal en cirugía rural
农村地区的个人相关提示
  • DOI:
  • 发表时间:
    2009
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Dana Christian Lynge;Eric Larson
  • 通讯作者:
    Eric Larson
Proceedings from the 9th annual conference on the science of dissemination and implementation
第九届传播与实施科学年会论文集
  • DOI:
  • 发表时间:
    2017
  • 期刊:
  • 影响因子:
    7.2
  • 作者:
    David A. Chambers;L. Simpson;G. Neta;U. V. T. Schwarz;Antoinette Percy;G. Aarons;R. Brownson;Amanda L. Vogel;S. Stirman;K. Sherr;R. Sturke;W. Norton;Allyson L. Varley;Cynthia A. Vinson;L. Klesges;S. Heurtin‐Roberts;M. Massoud;Leighann Kimble;A. Beck;Claire Neely;J. Boggs;C. Nichols;W. Wan;Erin M. Staab;N. Laiteerapong;Nathalie Moise;R. Shah;S. Essock;M. Handley;Amy Jones;Jay W Carruthers;K. Davidson;Lauren A. Peccoralo;L. Sederer;Todd Molfenter;Ashley T. Scudder;Sarah M. Taber;Kristen F. Schaffner;A. Herschell;Eva N. Woodward;J. Pitcock;Mona J. Ritchie;J. Kirchner;Julia E. Moore;Sobia Khan;S. Rashid;Jamie S. Park;Melissa Courvoisier;S. Straus;D. Blonigen;Allison L Rodriguez;Luisa Manfredi;A. Nevedal;J. Rosenthal;D. Smelson;C. Timko;N. Stadnick;Jennifer Regan;Miya L. Barnett;A. Lau;Lauren Brookman;E. Guerrero;Karissa M. Fenwick;Yinfei Kong;G. Aarons;Rebecca Lengnick;Benjamin F Henwood;N. Sayer;C. Rosen;Robert J Orazem;Brandy N. Smith;C. Rosen;L. Zimmerman;D. Lounsbury;C. Rosen;R. Kimerling;J. Trafton;S. Lindley;Rahul Bhargava;H. Roberts;Laura Gibson;G. Escobar;V. Liu;Benjamin Turk;Arona I. Ragins;P. Kipnis;Ashley Ketterer Gruszkowski;Michael W. Kennedy;Emily Rentschler Drobek;Lior Turgeman;A. Milićević;T. Hubert;L. Myaskovsky;Y. Tjader;Robert Monte;K. Sapnas;E. Ramly;D. Lauver;C. Bartels;Shereef M. Elnahal;A. Ippolito;H. Peabody;C. Clancy;R. Cebul;Thomas F. Love;D. Einstadter;S. Bolen;B. Watts;V. Yakovchenko;Angela M Park;William Lukesh;Donald R. Miller;D. Thornton;M. Drainoni;A. Gifford;Shawna N. Smith;Julia Kyle;M. Bauer;D. Eisenberg;Celeste Liebrecht;Michelle M Barbaresso;A. Kilbourne;E. Park;Giselle Perez;J. Ostroff;S. Greene;M. Parchman;Brian D. Austin;Eric Larson;S. Ferreri;C. Shea;Megan Smith;Kea Turner;J. Bacci;Kyle Bigham;G. Curran;Caity Frail;Cory Hamata;T. Jankowski;Wendy M. Lantaff;M. Mcgivney;M. Snyder;M. McCullough;C. Gillespie;B. A. Petrakis;Ellen A Jones;Angela M Park;C. V. Lukas;A. Rose;Sarah J. Shoemaker;Jeremy L Thomas;Benjamin S Teeter;Holly Swan;A. Balamurugan;M. Lane;R. Beidas;Laura J Di Taranti;Sruthi Buddai;Enrique Torres Hernandez;Jerome Watts;L. Fleisher;F. Barg;Isomi M. Miake;Tanya T. Olmos;Emmeline Chuang;Hector P Rodriguez;G. Kominski;B. Yano;S. Shortell;M. Hook;L. Fleisher;A. Fiks;Katherine Halkyard;Rachel S Gruver;Emily E Sykes;K. Vesco;Kate Beadle;J. Bulkley;Ashley B. Stoneburner;Michael Leo;Amanda L. Clark;J. Smith;C. Smyser;Maggie Wolf;S. Trivedi;B. Hackett;R. Rao;F. S. Cole;R. McGonigle;Ann Donze;E. Proctor;A. Mathur;K. Sherr;E. Gakidou;S. Gloyd;C. Audet;José Salato;S. Vermund;R. Amico;Stephanie L. Smith;B. Nyirandagijimana;H. Mukasakindi;C. Rusangwa;M. Franke;G. Raviola;M. Cummings;Elijah Goldberg;S. Mwaka;Olive Kabajaasi;A. Cattamanchi;A. Katamba;Shevin T. Jacob;N. Kenya;J. L. Davis;Julie E. Reed;R. Ramaswamy;G. Parry;S. Sax;H. Kaplan;K. Huang;Sabrina Cheng;Susan Yee;K. Hoagwood;M. McKay;D. Shelley;G. Ogedegbe;L. Brotman;R. Kislov;J. Humphreys;G. Harvey;Paul M. Wilson;Robert D. Lieberthal;C. Payton;M. Sarfaty;G. Valko;R. Bolton;C. V. Lukas;C. Hartmann;Nora M Mueller;Sally K. Holmes;B. Bokhour;Sarah S. Ono;B. Crabtree;Leah Gordon;William Miller;B. Balasubramanian;L. Solberg;D. Cohen;K. McGraw;Andrew Blatt;Demietrice Pittman;C. Hartmann;H. Kales;D. Berlowitz;T. Hudson;C. Helfrich;E. Finley;Ashley García;Kristen D. Rosen;C. Tami;Donald D. McGeary;M. Pugh;J. Potter;Krysttel C. Stryczek;D. Au;S. Zeliadt;G. Sayre;C. Gillespie;J. Leeman;Allison E. Myers;Jennifer C. Grant;Mary Wangen;Tara L Queen;A. Morshed;E. Dodson;R. Tabak;R. Brownson;R. C. Sheldrick;Thomas I. Mackie;Justeen K. Hyde;L. Leslie;Itzhak Yanovitzky;Matthew Weber;Nicole Gesualdo;Teis Kristensen;Cameo F. Stanick;Heather M. Halko;Caitlin N. Dorsey;B. Powell;B. Weiner;C. Lewis;S. Stirman;P. Carreno;Kera Mallard;Tasoula Masina;C. Monson;T. Swindle;Z. Patterson;Leanne Whiteside;R. Hanson;B. Saunders;Sonja K. Schoenwald;A. Moreland;S. Birken;B. Powell;J. Presseau;Isomi M. Miake;D. Ganz;B. Mittman;Deborah M Delevan;E. Finley;J. Hill;Sara M. Locatelli;G. Fix;J. Solomon;Sherri L. LaVela;V. Scott;J. Scaccia;K. Alia;Brittany Skiles;A. Wandersman;A. Sales;M. Roberts;Amy E. Kennedy;David A. Chambers;M. Khoury;N. Sperber;L. Orlando;J. Carpenter;L. Cavallari;J. Denny;Amanda Elsey;F. FitzHenry;Yue Guan;C. Horowitz;Julie A. Johnson;Ebony B. Madden;T. Pollin;Victoria S. Pratt;Tejinder K. Rakhra;M. Rosenman;C. Voils;K. Weitzel;R. Wu;L. Damschroder;Christine Y. Lu;Rachel Ceccarelli;K. Mazor;A. Wu;A. Rahm;A. Buchanan;Marci L. B. Schwartz;C. McCormick;Kandamurugu Manickam;Marc S. Williams;M. Murray;Ngoc;Erin Lebow;H. Udelson;Elaine A. Böing;Maria E. Fernandez;R. Wood;P. Mullen;J. Parekh;Valerie Caldas;E. Stuart;Shalynn Howard;Gilo Thomas;J. Jennings;Jennifer Torres;C. Markham;R. Shegog;Melissa F. Peskin;S. Rushing;Amanda Gaston;Gwenda Gorman;C. Jessen;J. Williamson;D. Ward;A. Vaughn;E. Morris;S. Mazzucca;Regan V. Burney;Shoba Ramanadhan;S. Minsky;Vilma Martinez;K. Viswanath;Megan Barker;Myra Fahim;Arezoo Ebnahmady;Rosa Dragonetti;P. Selby;M. Farrell;Jordan W. Tompkins;W. Norton;Kaelin Rapport;M. Hargreaves;Rebekka M. Lee;Shoba Ramanadhan;G. Kruse;C. Deutsch;E. Lanier;Ashley Gray;A. Leppin;Lori Christiansen;Karen S. Schaepe;Jason Egginton;M. Branda;C. Gaw;Sara R. Dick;V. Montori;Nilay Shah;Ariella R. Korn;P. Hovmand;Karen Fullerton;Nancy L. Zoellner;Erin Hennessy;Alison Tovar;Ross A. Hammond;C. Economos;Christi M. Kay;J. Gazmararian;E. Vall;Patricia C. Cheung;Padra A Franks;S. Barrett;Paul Weiss;E. Hamilton;E. Vall;L. Marques;L. Dixon;Emily M. Ahles;S. Valentine;C. Monson;D. Shtasel;S. Stirman;Rubén Parra;M. Northridge;Rucha Kavathe;Jennifer M. Zanowiak;Laura C. Wyatt;Hardayal Singh;N. Islam;Madalena Monteban;Darcy A. Freedman;Kimberly D. Bess;Colleen C. Walsh;K. Matlack;S. Flocke;H. Baily;S. Harden;NithyaPriya S Ramalingam;J. Scaccia;V. Scott;Rachel Gold;E. Cottrell;Celine Hollombe;Katie Dambrun;A. Bunce;M. Middendorf;Marla Dearing;S. Cowburn;Ned Mossman;Gerry Melgar;S. Hopfer;M. Hecht;Anne E. Ray;Michelle Miller;R. Belue;G. Zimet;E. Nelson;Sandy J Kuhlman;G. Doolittle;H. Krebill;A. Spaulding;Theodore Levin;Michael A. Sanchez;Molly A. E. Landau;Patricia R Escobar;N. Minian;Aliya Noormohamed;L. Zawertailo;D. Baliunas;N. Giesbrecht;B. Le Foll;A. Samokhvalov;Zachary F. Meisel;D. Polsky;B. Schackman;Julia Mitchell;Kaitlyn S. Sevarino;S. Gimbel;M. Mwanza;M. Nisingizwe;C. Michel;L. Hirschhorn;R. Beidas;Mahrukh Choudhary;Della Thonduparambil;P. Meissner;H. Pinnock;M. Barwick;C. Carpenter;S. Eldridge;G. Grandes;C. Griffiths;J. Rycroft;E. Murray;Anita Patel;A. Sheikh;Stephanie J. C. Taylor;B. Mittman;Martin Guilliford;Gemma Pearce;Diane M. Korngiebel;K. West;W. Burke;Peggy A. Hannon;Jeffrey H. Harris;Kristen Hammerback;M. Kohn;Gary K. C. Chan;Riki Mafune;Amanda T. Parrish;C. Helfrich;S. Beresford;K. J. Pike;R. Shelton;L. Jandorf;D. Erwin;Thana;M. Parchman;L. Baldwin;Brooke R Ike;Jacqueline J. Fickel;Jason D Lind;D. Cowper;Marguerite Fleming;A. Sadler;Melody Dye;Judith R. Katzburg;Michael K. Ong;Sarah Tubbesing;M. McCullough;Molly M. Simmons;V. Yakovchenko;Autumn Harnish;Sonya Gabrielian;K. McInnes;Jeffrey L. Smith;D. Smelson;John L Ferrand;Elisa M. Torres;A. Green;G. Aarons;A. Bradbury;L. Patrick;B. Egleston;S. Domchek;O. Olopade;M. Hall;M. Daly;L. Fleisher;G. Grana;P. Ganschow;D. Fetzer;Amanda Brandt;Rachelle Chambers;D. Clark;A. Forman;Rikki S. Gaber;C. Gulden;Janice Horte;Jessica M. Long;Terra Lucas;Shreshtha Madaan;Kristin Mattie;Danielle B. McKenna;Susan Montgomery;S. Nielsen;J. Powers;Kim Rainey;C. Rybak;Christina Seelaus;J. Stoll;J. Stopfer;X. Yao;Michelle Savage;Edward J. Miech;T. Damush;Nicholas A. Rattray;Jennifer Myers;Barbara J. Homoya;Kate Winseck;C. Klabunde;D. Langer;Avi Aggarwal;Elizabeth Neilson;Lara M Gunderson;Marla Gardner;Liam O’Sulleabhain;Candyce H Kroenke;P. Kipnis
  • 通讯作者:
    P. Kipnis
Generic Beauville’s Conjecture
一般博维尔猜想
  • DOI:
  • 发表时间:
    2023
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Izzet Coskun;Eric Larson;Isabel Vogt
  • 通讯作者:
    Isabel Vogt

Eric Larson的其他文献

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{{ truncateString('Eric Larson', 18)}}的其他基金

PostDoctoral Research Fellowship
博士后研究奖学金
  • 批准号:
    1802908
  • 财政年份:
    2018
  • 资助金额:
    $ 22.48万
  • 项目类别:
    Fellowship Award
EAPSI: A Home-and-Away Comparison of the Effects of an Invasive Crayfish on Aquatic Food Webs
EAPSI:入侵小龙虾对水生食物网影响的主场和客场比较
  • 批准号:
    0812976
  • 财政年份:
    2008
  • 资助金额:
    $ 22.48万
  • 项目类别:
    Fellowship Award
Support For Nsf Graduate Fellow
对 Nsf 研究生的支持
  • 批准号:
    8019074
  • 财政年份:
    1980
  • 资助金额:
    $ 22.48万
  • 项目类别:
    Fellowship Award
Support For Nsf Graduate Fellow
对 Nsf 研究生的支持
  • 批准号:
    7921341
  • 财政年份:
    1979
  • 资助金额:
    $ 22.48万
  • 项目类别:
    Fellowship Award
Support For Nsf Graduate Fellows
对 NSF 研究生的支持
  • 批准号:
    7821656
  • 财政年份:
    1978
  • 资助金额:
    $ 22.48万
  • 项目类别:
    Fellowship Award

相似海外基金

The embedded topology of projective plane curves and the generalization of splitting invariants
射影平面曲线的嵌入拓扑和分裂不变量的推广
  • 批准号:
    23K03042
  • 财政年份:
    2023
  • 资助金额:
    $ 22.48万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Weighted projective spaces and curves containing many rational points
包含许多有理点的加权射影空间和曲线
  • 批准号:
    551924-2020
  • 财政年份:
    2020
  • 资助金额:
    $ 22.48万
  • 项目类别:
    University Undergraduate Student Research Awards
Weighted projective spaces and curves containing many rational points
包含许多有理点的加权射影空间和曲线
  • 批准号:
    551923-2020
  • 财政年份:
    2020
  • 资助金额:
    $ 22.48万
  • 项目类别:
    University Undergraduate Student Research Awards
Derived-tame algebras and non-commutative nodal projective curves
导出驯服代数和非交换节点射影曲线
  • 批准号:
    283334198
  • 财政年份:
    2015
  • 资助金额:
    $ 22.48万
  • 项目类别:
    Research Grants
Projective models and automorphism groups on algebraic curves
代数曲线上的射影模型和自同构群
  • 批准号:
    15K04822
  • 财政年份:
    2015
  • 资助金额:
    $ 22.48万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Integral Points, Rational Curves and Entire Curves on Projective Varieties
射影簇上的积分点、有理曲线和整曲线
  • 批准号:
    1308737
  • 财政年份:
    2013
  • 资助金额:
    $ 22.48万
  • 项目类别:
    Standard Grant
Spaces of Rational Curves in Projective Varieties
射影簇中的有理曲线空间
  • 批准号:
    1204567
  • 财政年份:
    2012
  • 资助金额:
    $ 22.48万
  • 项目类别:
    Standard Grant
Linear Systems and Projective Models on Algebraic Curves
线性系统和代数曲线上的射影模型
  • 批准号:
    21540043
  • 财政年份:
    2009
  • 资助金额:
    $ 22.48万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Research on the geometry of the projective hypersutfaces and plane curves
射影超曲面与平面曲线的几何研究
  • 批准号:
    20540094
  • 财政年份:
    2008
  • 资助金额:
    $ 22.48万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Questions Related to Curves on Complex Projective Manifolds
与复射影流形上的曲线相关的问题
  • 批准号:
    0200895
  • 财政年份:
    2002
  • 资助金额:
    $ 22.48万
  • 项目类别:
    Continuing Grant
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