Algebraic Geometry Seminar Spring 2011: Difference between revisions
No edit summary |
No edit summary |
||
| Line 53: | Line 53: | ||
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. | ||
'''Anatoly Libgober''' ''Mordell Weil groups of iso-trivial abelian varieties and Alexander polynomials | '''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 | I will discuss a relation between the Mordell-Weil groups of isotrivial abelian varieties | ||
| Line 59: | Line 59: | ||
complement to ramification locus of the latter. The results are based on joint work | complement to ramification locus of the latter. The results are based on joint work | ||
with J.I.Cogolludo on families of elliptic curves. | with J.I.Cogolludo on families of elliptic curves. | ||
'''Valery Lunts''' ''Lefschetz fixed point theorems for algebraic varieties and DG algebras'' | |||
I will report on my work in progress about a version of Lefschetz fixed point theorem for | |||
morphisms (more generally for Fourier-Mukai transforms) of smooth projective varieties. There is also | |||
a parallel version for smooth and proper DG algebras. | |||
Revision as of 16:20, 25 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. 4 | Valery Lunts (Indiana-Bloomington) | TBA | Andrei Caldararu |
| Feb. 18 | Tony Várilly-Alvarado (Rice) | Failure of the Hasse principle for Enriques surfaces | David Brown |
| Feb. 25 | Bhargav Bhatt (UMich) | TBA | Jordan Ellenberg |
| Mar. 4 | Si Li (Harvard) | Higher Genus Mirror Symmetry | Junwu Tu |
| Mar. 25 | Srikanth Iyengar (Nebraska) | TBA | Andrei Caldararu |
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.
Valery Lunts Lefschetz fixed point theorems for algebraic varieties and DG algebras
I will report on my work in progress about a version of Lefschetz fixed point theorem for morphisms (more generally for Fourier-Mukai transforms) of smooth projective varieties. There is also a parallel version for smooth and proper DG algebras.