Algebraic geometry seminar
Day & Date: Monday, December 19, 2022.
Time: 4 pm.
Venue: Online talk at meet.google.com/vzr-ctov-kbs
Title: Seshadri constants over fields of characteristic zero
Speaker: Arghya Pramanik
Abstract: Let X be a smooth projective variety defined over a field k of
characteristic 0 and let L be a nef line bundle defined over k. In this
talk, I will show that if x ∈ X is a k-rational point then the Seshadri
constant ε(X, L, x) over \bar{k} is the same as that over k. I will also
construct families of varieties whose global Seshadri constant ε(X) is
zero. I also discuss a result on the existence of a Seshadri curve with a
natural (and necessary) hypothesis. In a recent paper, Fulger and Murayama
have defined a new version of Seshadri constants for vector bundles in a
relative setting over algebraically closed fields. We generalize the
definition for a general field and show that our results on line bundles
are also true for vector bundles. This talk is based on joint work with
Shripad M. Garge.