Algebraic Hyperbolicity and Lang Conjecture

代数双曲性和 Lang 猜想

• 批准号: RGPIN-2019-04775
• 负责人: Chen, Xi
• 金额: $ 1.24万
• 依托单位: University of Alberta
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2019
• 资助国家: 加拿大
• 起止时间: 2019-01-01 至 2020-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=675815
• 关键词: Algebraic; Hyperbolicity; Lang; Conjecture

Lang conjecture says that rational and elliptic curves on a variety of general type are algebraically***degenerate. We study this conjecture for generic hypersurfaces in projective spaces. This problem is***closely related to complex hyperbolicity and Kobayashi conjecture. In the algebraic setting, this amounts***to algebraic hyperbolicity in the sense of Demailly. H. Clemens proved that a generic hypersurface is***algebraically hyperbolic when the degree of the hypersurface is sufficiently large. We want to push his***bound on the degree of hypersurfaces to the conjectured optimum. We propose to approach this***conjecture by constructing the global jet spaces of versal families of hypersurfaces and studying the stable***loci of the corresponding jet bundles.

Lang猜想认为各种一般类型上的有理曲线和椭圆曲线在代数上是简并的。我们研究了射影空间中一般超曲面的这个猜想。这个问题与复双曲性和小林猜想密切相关。在代数环境中，这相当于Demailly意义上的代数双曲。H. Clemens证明了当超曲面的次足够大时，一般超曲面是***代数双曲的。我们想把他在超曲面度上的界推到推测的最优。我们提出通过构造一般超曲面族的全局喷流空间和研究相应喷流束的稳定轨迹来接近这个猜想。