Difference between revisions of "Algebraic Geometry Seminar Spring 2011"
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− | + | '''Anton Geraschenko''' "Toric Artin Stacks" | |
Toric varieties provide a fantastic testing ground for ideas about varieties. Their main feature is that geometric properties of toric varieties correspond to combinatorial properties of their fans. In this talk, I'll briefly review some facts about toric varieties, then define a notion of a stacky fan and the toric Artin stack associated to a stacky fan. I'll state and prove some results relating the combinatorics of the fan to the geometry of the stack and show some illustrative examples. If time permits, I'll motivate this notion of toric Artin stacks a bit more by discussing how toric Artin stacks defined by fans compare to possible intrinsic definitions of toric Artin stacks. Some experience with toric varieties or stacks is a plus, but not essential. | Toric varieties provide a fantastic testing ground for ideas about varieties. Their main feature is that geometric properties of toric varieties correspond to combinatorial properties of their fans. In this talk, I'll briefly review some facts about toric varieties, then define a notion of a stacky fan and the toric Artin stack associated to a stacky fan. I'll state and prove some results relating the combinatorics of the fan to the geometry of the stack and show some illustrative examples. If time permits, I'll motivate this notion of toric Artin stacks a bit more by discussing how toric Artin stacks defined by fans compare to possible intrinsic definitions of toric Artin stacks. Some experience with toric varieties or stacks is a plus, but not essential. |
Revision as of 13:16, 16 January 2011
The seminar meets on Fridays at 2:25 pm in Van Vleck B305.
The schedule for the previous semester is here.
Spring 2011
date | speaker | title | host(s) |
---|---|---|---|
Jan. 21 | Anton Geraschenko (UC Berkeley) | Toric Artin Stacks | David Brown |
Jan. 28 | Anatoly Libgober (UIC) | Mordell Weil groups of iso-trivial abelian varieties and Alexander polynomials. | Laurentiu Maxim |
Feb. 18 | Tony Várilly-Alvarado (Rice) | TBA | David Brown |
Feb. 25 | Bhargav Bhatt (UMich) | TBA | Jordan Ellenberg |
Abstracts
Anton Geraschenko "Toric Artin Stacks"
Toric varieties provide a fantastic testing ground for ideas about varieties. Their main feature is that geometric properties of toric varieties correspond to combinatorial properties of their fans. In this talk, I'll briefly review some facts about toric varieties, then define a notion of a stacky fan and the toric Artin stack associated to a stacky fan. I'll state and prove some results relating the combinatorics of the fan to the geometry of the stack and show some illustrative examples. If time permits, I'll motivate this notion of toric Artin stacks a bit more by discussing how toric Artin stacks defined by fans compare to possible intrinsic definitions of toric Artin stacks. Some experience with toric varieties or stacks is a plus, but not essential.
Anatoly Libgober Mordell Weil groups of iso-trivial abelian varieties and Alexander polynomials."
I will discuss a relation between the Mordell-Weil groups of isotrivial abelian varieties over function fields of cyclic coverings of projective plane and the Alexander polynomial of the complement to ramification locus of the latter. The results are based on joint work with J.I.Cogolludo on families of elliptic curves.