ICMS-Sofia and IMSA-Miami


Consortium Distinguished Lecture Series

PhilliGriffiths, Institute for Advanced Study, USA 

August 10, 2023, 15:15 (EEST, Sofia time),
IMI-BAS, Hall 403
and via Zoom

Period mappings for anti-canonical pairs

Abstract: Anti-canonical pairs (Y, D) are logarithmic K3 surfaces. It is well known that they have a rich geometry. A recent result, whose proof was motivated by mirror-symmetry, establishes a conjecture by Looijenga giving conditions for smoothability of the cusp obtained by contracting D. A central ingredient in the proof is a global Torelli theorem using the mixed Hodge structure on H2(Y −D). In this talk we will formulate and sketch the proof of this result.

*Based on the works of Looijenga [L81], Friedman [F16], Engel-Friedman [EF21], and Gross-Hacking-Keel [GHK15]. Presentation including notations, largely follows [F16].