Dan Abramovich: The Chow ring of a weighted blowup

Date: 2023-05-31

Time: 13:30 - 14:30

Zoom link: https://kva-se.zoom.us/j/9217561880


Dan Abramovich, Brown University


This is mostly a report on work of Brown PhD students Veronica Arena and Stephen Obinna.  The Chow groups of a blowup of a smooth variety along a smooth subvariety are described in Fulton’s book using Grothendieck’s “key formula”, involving the Chow groups of the blown up variety, the center of blowup, and the Chern classes of its normal bundle.  If interested in weighted blowups, one expects everything to generalize directly. This is in hindsight correct, except that at every turn there is an interesting and delightful surprise, shedding light on the original formulas for usual blowups, especially when one wants to pin down the integral Chow ring of a stack theoretic weighted blowup.  As an application, one obtains a quick derivation of a formula, due to Di Lorenzo-Pernice-Vistoli and Inchiostro, of the Chow ring of the moduli space $overline{M}_{1,2}$.