Topics in algebraic bundles

要考虑的第一个主题是基本尺寸的模栈束。几何对象的维数是一个重要的不变量。栈是普通空间的一个重要推广，当考虑对象的参数空间时自然出现。例如，曲线的最自然的参数“空间”实际上不是空间，而是堆栈。人们可以把堆栈看作是对称性的现代理论。对于栈，有两种维数的概念。经典尺寸，可以通过几十年前发展的变形理论的方法来计算。维数的第二个概念，本质维数，是一个更微妙的不变量。它是许多密集的工作和有趣的展览的中心。在我们的研究中，我们感兴趣的是研究代数曲线上的某些栈参数化丛的本质维数。

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.