代数几何研讨班

中科院数学与系统科学研究院

数学研究所

代数几何研讨班

报告人：李灵光 副教授（同济大学）

题  目：Introduction to the moduli spaces of vector bundles over an algebraic curve

时  间：2021.4.26（星期一），13:30-15:00

地  点：腾讯会议 434 627 441

摘  要：This talk contains four parts. In the first part, I will introduce some basic properties of vector bundles over algebraic curves. In the second part, I will give a review about the theory of Quot schemes. In the third part, I will give an introduction to the theory of geometric invariant theory. In the last part, I will give a construction of moduli spaces of vector bundles on an algebraic curve as a GIT quotient of a Quot scheme acted by a reductive group.
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  报告人：李灵光 副教授（同济大学）

题  目：Frobenius stratification of moduli spaces of vector bundles in positive characteristic.

时  间：2021.5.10（星期一），15:10-16:40

地  点：腾讯会议 672 940 562

摘  要：Let X be a smooth projective curve of genus g(X)>1 over an algebraically closed field k of characteristic p>0 and F_X:X->X bethe absolute Frobenius morphism. Let M^s_X(r,d) be the moduli space of stable vector bundles of rank r and degree d on X. We study the Frobenius stratification of M^s_X(r,d) in terms of Harder-Narasimhan polygons of Frobenius pull backs of stable vector bundles and get the irreducibility, smoothness and dimension of Frobenius strata in the case(p,g,r)=(3,2,3) with arbitrary d and the case (p,g,r,d)=(2,2,4,0).