Difference between revisions of "K3 Seminar Spring 2019"
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| bgcolor="#BCD2EE" | Title: Fourier-Mukai Transforms | | bgcolor="#BCD2EE" | Title: Fourier-Mukai Transforms | ||
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− | | bgcolor="#BCD2EE" | Abstract: I will describe Chow theoretic correspondences as a motivation to derived correspondences. We will then define integral functors on derived categories. The dual abelian variety will be given as a moduli space in terms of its functor of points, leading us to a definition of the universal Poincaré bundle on | + | | bgcolor="#BCD2EE" | Abstract: I will describe Chow theoretic correspondences as a motivation to derived correspondences. We will then define integral functors on derived categories. The dual abelian variety will be given as a moduli space in terms of its functor of points, leading us to a definition of the universal Poincaré bundle on Ax$\widehat{A}$^. The K-theoretic Fourier Mukai transform on elliptic curves will be computed. We will look at the integral transform from D(A) to D(A^) induced by the Poincaré bundle. Cohomology of the Poincaré bundle and the base change theorem will be stated and used to describe the Fourier-Mukai dual of a unipotent vector bundle on an abelian variety. For an elliptic curve E, we will establish the equivalence between |
1. the abelian category of semistable bundles of slope 0 on E, and | 1. the abelian category of semistable bundles of slope 0 on E, and | ||
2. the abelian category of coherent torsion sheaves on E. | 2. the abelian category of coherent torsion sheaves on E. |
Revision as of 16:30, 6 February 2019
When: Thursday 5-7 pm
Where: Van Vleck TBA
Schedule
Date | Speaker | Title |
March 7 | Mao Li | Basics of K3 Surfaces and the Grothendieck-Riemann-Roch theorem |
March 14 | Shengyuan Huang | Elliptic K3 Surfaces |
March 28 | Zheng Lu | Moduli of Stable Sheaves on a K3 Surface |
April 4 | Canberk Irimagzi | Fourier-Mukai Transforms |
April 11 | David Wagner | Cohomology of Complex K3 Surfaces and the Global Torelli Theorem |
April 25 | TBA | Derived Categories of K3 Surfaces |
March 7
Mao Li |
Title: Basics of K3 Surfaces and the Grothendieck-Riemann-Roch theorem |
Abstract: |
March 14
Shengyuan Huang |
Title: Elliptic K3 Surfaces |
Abstract: |
March 28
Zheng Lu |
Title: Moduli of Stable Sheaves on a K3 Surface |
Abstract: |
April 4
Canberk Irimagzi |
Title: Fourier-Mukai Transforms |
Abstract: I will describe Chow theoretic correspondences as a motivation to derived correspondences. We will then define integral functors on derived categories. The dual abelian variety will be given as a moduli space in terms of its functor of points, leading us to a definition of the universal Poincaré bundle on Ax$\widehat{A}$^. The K-theoretic Fourier Mukai transform on elliptic curves will be computed. We will look at the integral transform from D(A) to D(A^) induced by the Poincaré bundle. Cohomology of the Poincaré bundle and the base change theorem will be stated and used to describe the Fourier-Mukai dual of a unipotent vector bundle on an abelian variety. For an elliptic curve E, we will establish the equivalence between
1. the abelian category of semistable bundles of slope 0 on E, and 2. the abelian category of coherent torsion sheaves on E. Simple and indecomposable objects of these categories will be described (with the help of the structure theorem of PIDs) and we will deduce Atiyah’s classification of the indecomposable vector bundles of degree 0. |
April 11
David Wagner |
Title: Cohomology of Complex K3 Surfaces and the Global Torelli Theorem |
Abstract: |
April 25
TBA |
Title: Derived Categories of K3 Surfaces |
Abstract: |
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