Kontsevich-Type Recursions for Counts of Real Curves
报告人：Xujia Chen (Stony Brook)
时间：2018-12-19 14:00 - 2018-12-19 16:00
地点：Room 29, Quan Zhai, BICMR
Kontsevich\'s recursion, proved by Ruan-Tian in the early 90s, enumerates rational curves in complex surfaces. Welschinger defined invariant signed counts of real rational curves in real surfaces (complex surfaces with a conjugation) in 2003. Solomon interpreted Welschinger\'s invariants as holomorphic disk counts in 2006 and proposed Kontsevich-type recursions for them in 2007, along with an outline for adapting Ruan-Tian\'s homotopy style argument to the real setting. For many symplectic fourfolds, these recursions determine all invariants from basic inputs. We establish Solomon\'s recursions by re-interpreting his disk counts as degrees of relatively oriented pseudocycles from moduli spaces of stable real maps and lifting cobordisms from Deligne-Mumford moduli spaces of stable real curves.