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Speaker: Kamryn Spinelli

Affiliation: ³ÉÈË´óƬ

Title: Invariant-theoretic period integrals of CY branched covers of projective spaces

Abstract: In this talk, we will derive explicit hypergeometric formulas for the periods of CY double covers of projective spaces \mathbb{P}^{n-1} branched over 2n hyperplanes. This is a broad class of CY spaces including elliptic curves, K3 surfaces of Picard number 16, and some Calabi-Yau threefolds, to name a few. While some specific "gauge-fixed" cases have been analyzed before, no general expression for the full family has yet appeared. Our key insight is that the invariant theory encoded in the tautological system governing the periods of these families enables one to lift a restricted hypergeometric period formula derived by Matsumoto, Sasaki, and Yoshida from a closed subvariety of the parameter space. This is joint work with Bong Lian.