Hyperbolicity and classification theory in complex algebraic geometry

复代数几何中的双曲性和分类理论

基本信息

  • 批准号:
    170276-2010
  • 负责人:
  • 金额:
    $ 1.09万
  • 依托单位:
  • 依托单位国家:
    加拿大
  • 项目类别:
    Discovery Grants Program - Individual
  • 财政年份:
    2013
  • 资助国家:
    加拿大
  • 起止时间:
    2013-01-01 至 2014-12-31
  • 项目状态:
    已结题

项目摘要

My work involves the structure and classification of algebraic varieties, which are objects defined by homogeneous polynomials, up to a natural equivalence, called birational equivalence. Two such objects are birationally equivalent if their spaces of rational functions, are naturally isomorphic. The behavior of holomorphic (i.e., complex differentiable) or algebraic functions from the complex number plane with values in them lies at the center of my investigation. Besides the classical motivation of generalizing Picard's theorems (Lang's conjecture on the pseudo-hyperbolicity of varieties of general type), there is also strong motivation from number theory, such as the Mordell conjecture on the finiteness of solutions to a set of polynomials in terms of rational numbers if the variety defined is a curve of general type (solved by G. Faltings, for which he obtained the highest honor in Mathematics, the Fields Medal). Faltings gave two solutions to the Mordell conjecture, the second using an idea of Vojta-Mazur on the parallel between the value distribution theory of holomorphic curves, Pioneered by Nevanlinna, and the distribution of rational or algebraic points (i.e. solutions by integers or by radicals of integers of the homogeneous equations defining the variety). It is therefore hoped that a deeper understanding of the structure of curves in an algebraic variety would eventually lead to unlocking the mysteries of the similarities seen between natural questions in number theory and those concerning the behavior of holomorphic and algebraic curves.
我的工作涉及代数品种的结构和分类,它们是由均质多项式定义的对象,直至自然等效,称为Birational等价。如果有两个这样的对象,如果它们的理性函数空间自然是同构的,则是同等的。与复数平面相关的圆周形态(即,复杂的可分化)或代数函数的行为在于我的研究中心。 Besides the classical motivation of generalizing Picard's theorems (Lang's conjecture on the pseudo-hyperbolicity of varieties of general type), there is also strong motivation from number theory, such as the Mordell conjecture on the finiteness of solutions to a set of polynomials in terms of rational numbers if the variety defined is a curve of general type (solved by G. Faltings, for which he obtained the highest honor in数学,领域奖章)。 Faltings为Mordell的猜想提供了两种解决方案,第二种方法是使用Vojta-Mazur的概念,在尼凡林纳纳(Nevanlinna)的圆锥形曲线的价值分布理论和理性或代数点之间的分布(即,整数或由整数的解决方案或由整体的分布)定义了各种综述。因此,希望对代数品种中曲线的结构有更深入的了解最终会导致释放数字理论中自然问题与关于霍顿和代数曲线行为的相似之处的奥秘。

项目成果

期刊论文数量(0)
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Lu, Steven其他文献

Synthetic biodegradable hydrogel delivery of demineralized bone matrix for bone augmentation in a rat model.
  • DOI:
    10.1016/j.actbio.2014.07.011
  • 发表时间:
    2014-11
  • 期刊:
  • 影响因子:
    9.7
  • 作者:
    Kinard, Lucas A.;Dahlin, Rebecca L.;Lam, Johnny;Lu, Steven;Lee, Esther J.;Kasper, F. Kurtis;Mikos, Antonios G.
  • 通讯作者:
    Mikos, Antonios G.
Osteochondral tissue regeneration through polymeric delivery of DNA encoding for the SOX trio and RUNX2.
  • DOI:
    10.1016/j.actbio.2014.05.011
  • 发表时间:
    2014-10
  • 期刊:
  • 影响因子:
    9.7
  • 作者:
    Needham, Clark J.;Shah, Santa R.;Dahlin, Rebecca L.;Kinard, Lucas A.;Lam, Johnny;Watson, Brendan M.;Lu, Steven;Kasper, F. Kurtis;Mikos, Antonios G.
  • 通讯作者:
    Mikos, Antonios G.
Short term outcomes and unintended benefits of establishing a HPB program at a university-affiliated community hospital
  • DOI:
    10.1016/j.amjsurg.2019.03.015
  • 发表时间:
    2019-11-01
  • 期刊:
  • 影响因子:
    3
  • 作者:
    Lu, Steven;Khatri, Richa;Munene, Gitonga
  • 通讯作者:
    Munene, Gitonga
Fabrication of Cell-Laden Macroporous Biodegradable Hydrogels with Tunable Porosities and Pore Sizes
  • DOI:
    10.1089/ten.tec.2014.0224
  • 发表时间:
    2015-03-01
  • 期刊:
  • 影响因子:
    3
  • 作者:
    Wang, Limin;Lu, Steven;Mikos, Antonios G.
  • 通讯作者:
    Mikos, Antonios G.
Articular chondrocytes and mesenchymal stem cells seeded on biodegradable scaffolds for the repair of cartilage in a rat osteochondral defect model.
  • DOI:
    10.1016/j.biomaterials.2014.05.055
  • 发表时间:
    2014-08
  • 期刊:
  • 影响因子:
    14
  • 作者:
    Dahlin, Rebecca L.;Kinard, Lucas A.;Lam, Johnny;Needham, Clark J.;Lu, Steven;Kasper, F. Kurtis;Mikos, Antonios G.
  • 通讯作者:
    Mikos, Antonios G.

Lu, Steven的其他文献

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{{ truncateString('Lu, Steven', 18)}}的其他基金

Complex geometry of orbifold pairs and of their moduli spaces; structure, classification and relation to arithmetic geometry
轨道对及其模空间的复杂几何;
  • 批准号:
    RGPIN-2022-05387
  • 财政年份:
    2022
  • 资助金额:
    $ 1.09万
  • 项目类别:
    Discovery Grants Program - Individual
Generalized hyperbolicity and the geometry of algebraic varieties
广义双曲性和代数簇的几何
  • 批准号:
    RGPIN-2016-05294
  • 财政年份:
    2021
  • 资助金额:
    $ 1.09万
  • 项目类别:
    Discovery Grants Program - Individual
Generalized hyperbolicity and the geometry of algebraic varieties
广义双曲性和代数簇的几何
  • 批准号:
    RGPIN-2016-05294
  • 财政年份:
    2020
  • 资助金额:
    $ 1.09万
  • 项目类别:
    Discovery Grants Program - Individual
Generalized hyperbolicity and the geometry of algebraic varieties
广义双曲性和代数簇的几何
  • 批准号:
    RGPIN-2016-05294
  • 财政年份:
    2019
  • 资助金额:
    $ 1.09万
  • 项目类别:
    Discovery Grants Program - Individual
Generalized hyperbolicity and the geometry of algebraic varieties
广义双曲性和代数簇的几何
  • 批准号:
    RGPIN-2016-05294
  • 财政年份:
    2018
  • 资助金额:
    $ 1.09万
  • 项目类别:
    Discovery Grants Program - Individual
Generalized hyperbolicity and the geometry of algebraic varieties
广义双曲性和代数簇的几何
  • 批准号:
    RGPIN-2016-05294
  • 财政年份:
    2017
  • 资助金额:
    $ 1.09万
  • 项目类别:
    Discovery Grants Program - Individual
Generalized hyperbolicity and the geometry of algebraic varieties
广义双曲性和代数簇的几何
  • 批准号:
    RGPIN-2016-05294
  • 财政年份:
    2016
  • 资助金额:
    $ 1.09万
  • 项目类别:
    Discovery Grants Program - Individual
Hyperbolicity and classification theory in complex algebraic geometry
复代数几何中的双曲性和分类理论
  • 批准号:
    170276-2010
  • 财政年份:
    2014
  • 资助金额:
    $ 1.09万
  • 项目类别:
    Discovery Grants Program - Individual
Hyperbolicity and classification theory in complex algebraic geometry
复代数几何中的双曲性和分类理论
  • 批准号:
    170276-2010
  • 财政年份:
    2012
  • 资助金额:
    $ 1.09万
  • 项目类别:
    Discovery Grants Program - Individual
Hyperbolicity and classification theory in complex algebraic geometry
复代数几何中的双曲性和分类理论
  • 批准号:
    170276-2010
  • 财政年份:
    2011
  • 资助金额:
    $ 1.09万
  • 项目类别:
    Discovery Grants Program - Individual

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