Speaker: Sergey Galkin

Title: Joins and Hadamard products

Date: Sep 17, 2015, 16:30 - 17:30

Place: Steklov Mathematical Institute

I will discuss a procedure of creating new deformation classes of projective varieties by smoothing a join of two known ones. This way starting from two elliptic curves one can obtain various interesting Calabi-Yau threefolds, some are non-simply-connected. Also this explains that Calabi-Yau threefolds of degree 25, obtained as intersection of two Grassmannians in P^9, are in fact linear sections of a smooth Fano sixfold. In a sense, this procedure is a generalization of complete intersection for non-hypersurface case. I will explain why quantum periods of such new Calabi-Yau varieties are Hadamard products of the quantum periods of original pieces. Also if the original varieties had mirror-dual functions f(x) and g(y), then a smoothing of a join will have mirror-dual function given by exterior product f(x) g(y).