Abstract: We discuss the definition and basic props. of the above mentioned concepts and some important consequences.
Thursday, April 11th
Ed Karasiewicz, Rutgers
"Endomorphisms of Abelian varieties"
Time: 5:00 PM
Location: Hill 425
Abstract: We study the ring of endomorphisms of abelian varieties, their isogenous decompositions, and applications to other geometric aspects of abelian varieties.
Thursday, March 28th
Zhuohui Zhang, Rutgers University
"An exact sequence for dual abelian varieties"
Time: 5:00 PM
Location: Hill 425
Abstract: *This should be a nicer post*
My intention is to prove that for any isogeny f: X-> Y between abelian varieties, there is a canonical duality between its kernel and the kernel of the corresponding isogeny from dual of Y to dual of X. There are two approaches of doing this. One way is to assume the characteristic of the field is zero so that there are no problem for isogenies to be separated. Another way is to work with varieties over general fields, but this would require more mechanics. I will mainly work on the first way, but I would offer an invitation to the second way.
Thursday, March 14th
Sjuvon Chung, Rutgers
"Dual Abelian Varieties"
Time: 5:00 PM
Location: Hill 425
Abstract: Having developed the necessary background on quotients, we finally construct the dual abelian variety and show that it represents the Pic^0 functor.
Thursday, March 7th
Howard Nuer, Rutgers
"Dual Abelian Varieties (Part II)"
Time: 5:00 PM
Location: Hill 425
Abstract: We continue our discussion from last week and show how to use the theory of finite group quotients to construct the dual abelian variety (at least in char 0).
Thursday, February 28th
Howard Nuer, Rutgers
"Quotients of Varieties by finite groups and the Dual Abelian Variety"
Time: 5:00 PM
Location: Hill 425
Abstract: We first discuss the important construction of a "geometric quotient" of a variety by a finite group and some consequences for it's category of coherent sheaves. We use this to construct the dual abelian variety of a given abelian variety along with the so-called Poincare bundle.
Thursday, February 21st
Knight Fu, Rutgers
"Isogenies of Abelian Varieties"
Time: 5:00 PM
Location: Hill 425
Abstract: We discuss isogenies of Abelian varieties over fields of arbitrary characteristic, generalizing our discussion in the simple case of complex tori.
Thursday, February 14th
Ed Karasiewicz, Rutgers
"Projectivity of Abelian Varieties"
Time: 5:00 PM
Location: Hill 101
Abstract: We discuss the existence of ample line bundles on Abelian varieties.
Thursday, February 7th
Howard Nuer/Zhuohui Zhang, Rutgers
"Birational geometry of Abelian Varieties/Theorem of the Cube and its consequences"
Time: 5:00 PM
Location: Hill 425
Abstract: We'll finish up with some of the basic geometry of abelian varieties by seeing that they have very uninteresting birational geometry. Then we'll discuss the Theorem of the Cube and its consequences for understanding line bundles on abelian varieties.
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