Bott vanishing using GIT and quantization

Abstract: A smooth projective variety is said to satisfy Bott vanishing if $\Omega^j\otimes L$ has no higher cohomology for every $j$ and every ample line bundle $L$. This is a very restrictive property, and there are few non-toric examples known to satisfy it. I will present a new class of examples obtained as smooth GIT quotients of $(\mathbb{P}^{1})^n$. For this, I will need to use the work by Teleman and Halpern-Leistner about the derived category of a GIT quotient, and explain how this allows us, in some cases, to compute cohomologies directly in an ambient quotient stack.

algebraic geometry

Audience: researchers in the discipline

American Graduate Student Algebraic Geometry Seminar

Series comments: The American Graduate Student Algebraic Geometry Seminar (AGSAGS) is a virtual seminar by and for algebraic geometry graduate students.

The goal of this seminar is for graduate students to share their research through online talks and to provide an algebraic geometry graduate networking system. Grad students, postdocs, and professors are welcome to attend.

Seminars will be held on Mondays at 4 p.m. Eastern on Zoom. We hope this time is convenient for graduate students in the Americas, hence the name AGSAGS. Prior registration is required and interested participants should register here: sites.google.com/view/agsags/registration. In addition to graduate talks, there will be occasional social events.