Enriques manifolds

恩里克流形

• 批准号: 248329530
• 负责人: Professor Dr. Stefan Schröer
• 金额: --
• 依托单位: Lehrstuhl für Algebraische Geometrie
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2013
• 资助国家: 德国
• 起止时间: 2012-12-31 至 2019-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/248329530?language=en
• 关键词: Enriques; manifolds

Enriques surfaces comprise one of the four fundamental classes of algebraic surfaces whose tangential bundle is numerically trivial, and is to date subject of intensive research.Recently, the notion of Enriques surfaces was generalized to higher dimensions, with the help of hyperkähler manifolds.In this research project we shall investigate certain arithmetic and geometric properties of Enriques surfaces and Enriques manifolds.One research goal is to determine whether or not special Enriques surfaces are definable by polynomial equations with integral coefficients so that no singularities arise at all finite primes. By results of Fontaine, this is indeed impossible for the related classes of algebraic surfaces.Further goals are to construct new and more complicated examples for Enriques manifolds, and to develop a theory of Enriques manifolds in positive characteristics.

Enriques曲面是代数曲面的四种基本类型之一，它的切丛在数值上是平凡的，并且是迄今为止深入研究的主题。最近，Enriques曲面的概念被推广到高维，在这个研究项目中，我们将研究Enriques曲面和Enriques流形的某些算术和几何性质。一个研究目标是确定特殊的Enriques曲面是否可由整系数的多项式方程定义，使得在所有有限素数处都不会出现奇点。根据方丹的结果，这对于相关的代数曲面类确实是不可能的.进一步的目标是构造新的更复杂的Enriques流形的例子，并发展正特征的Enriques流形理论.

项目成果

The torsion in the cohomology of wild elliptic fibers

野生椭圆纤维上同调中的扭转

• DOI: 10.1016/j.jpaa.2020.106522
• 发表时间: 2021
• 期刊: arXiv: Algebraic Geometry
• 作者: Zimmermann

On equivariant formal deformation theory

等变形式变形理论

• DOI: 10.1007/s12215-017-0322-x
• 发表时间: 2018
• 期刊: Rendiconti del Circolo Matematico di Palermo Series 2
• 作者: Schröer;Takayama
• 通讯作者: Takayama

Enriques surfaces with normal K3-like coverings

Enrique 的表面具有正常的类似 K3 的覆盖物

• DOI: 10.2969/jmsj/83728372
• 发表时间: 2017
• 期刊: Journal of the Mathematical Society of Japan
• 影响因子: 0.7
• 作者: Schröer