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Carlos Simpson:Moduli Spaces of Sheaves on Surfaces——Lectures 1-2
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https://www.youtube.com/watch?v=79N4deKRYJE FRG讲座 Homepage:http://homepages.math.uic.edu/~coskun/frgcsimpson.html Carlos Simpson——《Lectures on Moduli Spaces of Sheaves on Surfaces》Slides:http://homepages.math.uic.edu/~coskun/moduliTalks-2.pdf 一: Moduli spaces of sheaves-an overview of the geography 摘要:In this first talk we will look more globally at the properties of moduli spaces of vector bundles and sheaves on various kinds of varieties, then specializing to the case of surfaces and in particular the case of rank 2 bundles on quintic hypersurfaces in P^3 二: Constructions and local properties: the Cayley-Bacharach condition 摘要:In the second talk, we look at the Serre construction of rank 2 vector bundles using the Cayley-Bacharach condition on zero-dimensional subschemes. Topics include the local deformation theory, how it interacts with the Serre construction, and the interpretation of co-obstructions as Higgs fields 三: Ascending induction and O'Grady's method 摘要:In the third talk, we introduce O'Grady's method of deforming to the boundary by creating deformations from bundles to torsion-free sheaves. Combining that with explicit constructions for low values of c_2, we look at the implications for the how the collection of moduli spaces fits together as c_2 increases 四: Structure of the moduli spaces and their boundaries 摘要:The fourth talk combines the previous strands to obtain the picture of the moduli spaces of rank 2 bundles and sheaves of odd degree on a quintic hypersurface. Further questions are explored Carlos Simpson是一位著名的美国数学家,专门研究代数几何。他于1987年在哈佛大学获得数学博士学位,由W.Schmid指导。他先后在法国图卢兹第三大学和法国尼斯大学担任教授。他是法国国家科学研究中心CNRS的研究主任。他致力于向量丛的模空间、高阶非阿贝尔de Rham上同调 (Hodge理论)和Higher category理论。在他的博士论文中,他研究了Hodge bundles系统的概念,这可以被视为N.Hitchin早些时候引入的Higgs bundles的高维推广的一个特例。Corlette-Simpson correspondence是Higgs bundles和光滑复代数曲线的基本群的表示之间的对应关系。Deligne–Simpson Problem是一个与monodromy matrices相关的代数问题,以C.Simpson和P.Deligne的名字命名。他是1990年在京都举行的国际数学家大会上受邀演讲《Nonabelian Hodge theory》的演讲者。
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