Minimal Model Program in Birational Geometry

双有理几何最小模型程序

• 批准号: EP/I004092/1
• 负责人: Paolo Cascini
• 金额: $ 10.7万
• 依托单位: Imperial College London
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2011
• 资助国家: 英国
• 起止时间: 2011 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FI004092%2F1
• 关键词: Minimal; Model; Program; Birational; Geometry

Algebraic Geometry is the study of algebraic varieties, i.e. the setof points satisfying a system of polynomial equations. In the last two decades, algebraic geometry has played a central role in Mathematics, due to its many applications in different fields. Thus, it is of crucial importance to find a classification of thesevarieties. The Minimal Model Program, started by Mori around the 1970's, aims to generalize the classification of projective surfaces,i.e. two dimensional projective varieties, to higher dimensional varieties. This Program was successfully carried out in the 1980's for projectivethree-folds, i.e. projective varieties of dimension three. In higher dimension, many problems concerning the geometry of projective varieties are still open. The proposed research aims to solve some of these outstanding problems, making progress in the Minimal Model Program.

代数几何是研究代数簇，即满足多项式方程组的点集。在过去的二十年里，代数几何在数学中发挥了核心作用，因为它在不同领域的许多应用。因此，对这些品种进行分类是至关重要的。由Mori在20世纪70年代开始的最小模型程序旨在将投影曲面的分类，即二维投影簇，推广到高维簇。这个程序在20世纪80年代成功地进行了三重投影，即三维投影簇。在高维空间中，关于射影簇几何的许多问题仍然是悬而未决的。本研究旨在解决其中的一些突出问题，在最小模型计划方面取得进展。

项目成果

The Augmented Base Locus in Positive Characteristic

• DOI: 10.1017/s0013091513000916
• 发表时间: 2011-11
• 期刊: Proceedings of the Edinburgh Mathematical Society
• 影响因子: 0.7
• 作者: P. Cascini;J. McKernan;M. Mustaţă

On the Chern numbers of a smooth threefold

• DOI: 10.1090/tran/7216
• 发表时间: 2014-12
• 期刊: arXiv: Algebraic Geometry
• 作者: Paolo Cascini;L. Tasin

Uniform bounds for strongly $F$-regular surfaces

强 $F$ 规则曲面的统一边界

• DOI: 10.1090/tran/6515
• 发表时间: 2014
• 期刊: arXiv: Algebraic Geometry
• 作者: Paolo Cascini;Yoshinori Gongyo;Karl Schwede
• 通讯作者: Karl Schwede

Symplectic generic complex structures on four-manifolds with $b_+ = 1$

$b_ = 1$ 的四流形上的辛泛复结构

• DOI: 10.4310/jsg.2012.v10.n4.a1
• 发表时间: 2012
• 期刊: Journal of Symplectic Geometry
• 影响因子: 0.7
• 作者: Cascini P

Seshadri constants on smooth threefolds

光滑三重上的 Seshadri 常数

• DOI: 10.1515/advgeom-2013-0012
• 发表时间: 2014
• 期刊: advg
• 作者: Cascini P