SAG: Bézout's theorem for abelian varietiesSeminar Algebraic Geometry (SAG)

by Ben Moonen (Nijmegen)

Thursday Oct 15, 2026, 10:30 AM → 11:30 AM Europe/Berlin

MPIM, Vivatsgasse, 7 - Lecture Hall (Max Planck Institute for Mathematics)

Abstract: I'll report on joint work with Olivier Debarre. The main result is that if A is an absolutely simple abelian variety over some field and X,Y are subvarieties of A, then the dimension of their sum X+Y equals the minimum of dim(A) and dim(X)+dim(Y). In characteristic 0, there is a very nice geometric proof, but that argument breaks down in characteristic p. Instead, we prove this result as a consequence of a theorem about perverse sheaves, building upon work of Krämer and Weissauer