Splitting types of finite monodromy vector bundles

Fri Feb 10, 20:00-21:00 (3 days from now)
Lecture held in Room 383-N.

Abstract: Given a finite degree $d$ cover of curves $f: X \to \mathbb P^1$, we study $f_* \mathscr O_X$, which is a rank $d$ vector bundle on $\mathbb P^1$, hence can be written as a direct sum of line bundles $f_* \mathscr O_X \simeq \oplus_{i=1}^d \mathscr O(a_i)$. Naively, one might expect that if the cover above is general, this vector bundle is balanced, meaning that the $a_i$'s are as close to each other as possible. While this is not quite true, we explain what can be said about these splitting types, by studying how they change as we deform the cover. This is based on joint work with Daniel Litt.

The ideas cropping up here were also instrumental in resolving conjectures of Esnault-Kerz and Budur-Wang regarding the density of geometric local systems in the moduli space of local systems.

algebraic geometry

Audience: researchers in the topic

( paper )


Stanford algebraic geometry seminar

Series comments: This seminar requires both advance registration, and a password. Register at stanford.zoom.us/meeting/register/tJEvcOuprz8vHtbL2_TTgZzr-_UhGvnr1EGv Password: 362880

If you have registered once, you are always registered for the seminar, and can join any future talk using the link you receive by email. If you lose the link, feel free to reregister. This might work too: stanford.zoom.us/j/95272114542

More seminar information (including slides and videos, when available): agstanford.com

Organizer: Ravi Vakil*
*contact for this listing

Export talk to