Topics in algebraic bundles

代数丛中的主题

• 批准号: 327639-2011
• 负责人: Dhillon, Ajneet
• 金额: $ 1.09万
• 依托单位: University of Western Ontario
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2014
• 资助国家: 加拿大
• 起止时间: 2014-01-01 至 2015-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=549155
• 关键词: Topics; algebraic; bundles

The first topic to be considered is the essential dimension of moduli stacks of bundles. The dimension of a geometrical object is an important invariant. Stacks are an important generalisation of ordinary spaces that arise naturally when considering parameter spaces for objects. For example the most natural parameter "space" for curves is in fact not a space but a stack. One may view stacks as a modern theory of symmetries. For stacks there are two notions of dimension. Classical dimension, can be computed via methods from deformation theory that were developed many decades ago. The second notion of dimension, essential dimension, turns out to be a far more subtle invariant. It is the center of much intensive work and interesting conjectures. In our research we are interested in studying the essential dimension of certain stacks parametrising bundles over algebraic curves.

要考虑的第一个主题是束模堆栈的基本维度。几何对象的尺寸是一个重要的不变量。堆栈是普通空间的重要概括，在考虑对象的参数空间时自然出现。例如，曲线最自然的参数“空间”实际上不是空间而是堆栈。人们可能将堆栈视为一种现代对称理论。对于堆栈有两个维度概念。经典尺寸可以通过几十年前开发的变形理论的方法来计算。维度的第二个概念，本质维度，被证明是一个更加微妙的不变量。它是大量密集工作和有趣猜想的中心。在我们的研究中，我们有兴趣研究代数曲线上某些堆栈参数化丛的基本维度。