Speaker: Sergey Galkin
Title: Joins and Hadamard products
Date: May 23, 2015, 14:00
Place: Istanbul Centre for Mathematical Sciences, Bosphorus University
Given two elliptic curves of small degree I will smooth out their join to obtain new (and old) interesting (and boring) examples of Calabi-Yau threefolds. Then I also explain how the generating function for the numbers of rational curves on these threefolds is related to the Hadamard product of the generating functions of rational curves on the respective elliptic curves (or, rather, their enveloping del Pezzo surfaces). The construction of mirrors for these threefolds is also very straightforward: the respective potential has form F(x) G(y), where F(x) and G(y) are mirror potentials to the original elliptic curves. Existence of some of CY3 with the respective Gromov-Witten invariants (respectively, periods) was predicted by Mainz group (van Enckewort, van Straten, Almkvist, Zudlin, …). The construction also works for smoothing some other joins and computing their Gromov—Witten invariants, double covers being another interesting example.