Foliation Theory in Birational Geometry

双有理几何中的叶理理论

• 批准号: EP/J019356/1
• 负责人: Paolo Cascini
• 金额: $ 27.85万
• 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: 2013
• 资助国家: 英国
• 起止时间: 2013 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FJ019356%2F1
• 关键词: Foliation; Theory; Birational; Geometry

The goal of the Minimal Model Program is to generalise the main results of the Castelnuovo-Enrique-Severi classification of algebraic surfaces, to higher dimensional projective varieties. The programme was started by Mori in the 1980s, for which he won the prestigious Fields Medal. It was successfully carried out for projective threefolds by Kawamata, Kollár, Miyaoka, Mori, Reid, Shokurov and many others. More recently, some of these results were also generalised to any dimension.The purpose of the proposed research is to develop new techniques, usingFoliation Theory, to solve some of the current obstacles in the MinimalModel Program. This will be achieved by combining together tools from different areas of mathematics, such as Number Theory, Kähler Geometry and Analysis. In particular, I plan to use the new results in the Minimal Model Program to study the classification of foliations over a projective variety.

最小模型程序的目标是概括的主要成果的Castelnuovo-恩里克-塞维里分类的代数曲面，更高的维度投影品种。该计划由Mori在20世纪80年代开始，为此他赢得了着名的菲尔兹奖。这是成功地进行了投影三倍由川又，Kollár，宫冈，森，里德，Shokurov和许多其他人。最近，其中一些结果也被推广到任何dimension.The建议的研究的目的是开发新的技术，usingFoliation理论，以解决目前的一些障碍，在MinimalModel程序。这将通过将来自不同数学领域的工具结合在一起来实现，例如数论，Kähler几何和分析。特别是，我计划使用的最小模型程序中的新成果，研究的分类叶理的投影品种。

项目成果

Effective finite generation for adjoint rings

• DOI: 10.5802/aif.2841
• 发表时间: 2012-03
• 期刊: arXiv: Algebraic Geometry
• 作者: Paolo Cascini;De-Qi Zhang

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

Foliation Theory in Algebraic Geometry

代数几何中的叶层理论

• 发表时间: 2015
• 作者: Cascini P.

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

A remark on the Ueno-Campana's threefold

关于上诺-坎帕纳三重的评论

• 发表时间: 2016
• 期刊: Michigan Math. Journal
• 作者: Bisi C.