Mirror symmetry for log Calabi-Yau surfaces II
Time: 2022-04-13
Published By: Wenqiong Li
Speaker(s): Yan Zhou(Peking University)
Time: 14:00-15:00 April 19, 2022
Venue: Room 29, Quan Zhai, BICMR
In 'Mirror symmetry for log Calabi-Yau surfaces I', given a log Calabi-Yau surface pair (Y,D), Gross-Hacking-Keel constructed its mirror family as the spectrum of an explicit algebra whose structure coefficients are determined by the enumerative geometry of (Y,D). As a follow-up of the work of Gross-Hacking-Keel, when (Y,D) is positive, we prove the modularity of the mirror family as the universal family of (Y,D). As a corollary, we show that the ring of regular functions of an affine log Calabi-Yau surface has a canonical basis of theta functions. The key step towards the proof of the main theorem is the application of the tropical construction of singular cycles and explicit formulas of period integrals given in the work of Helge-Siebert. This is joint work with Jonathan Lai.
