Adrian Zahariuc (University of Windsor)

Algebra & Geometry Seminar

Speaker: Adrian Zahariuc (University of Windsor)

Title: Interpolation of fat points on K3 and abelian surfaces

Abstract: This talk will be concerned with questions in the style of the Segre-Harbourne-Gimigliano-Hirschowitz (SHGH) Conjecture. I will sketch a proof of the fact that any number of general fat points of any multiplicities impose the expected number of conditions on the primitive linear system of a very general K3 or abelian surfaces of any degree/polarization. The proof relies on the Segal-Wilson formula for the vanishing of the theta function in the KP direction, and thus has a significant (although implicit) transcendental ingredient.