**CANCELED** Lifting cobordisms and Kontsevich-type recursions for counts of real curves **CANCELED**


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March 17, 2020 11:00 am - 12:00 pm

Xujia Chen - Stony Brook University

Kontsevich's recursion, proved in the early 90s, is a recursion formula for the counts of rational holomorphic curves in complex manifolds. For complex fourfolds and sixfolds with a real structure (i.e. a conjugation), signed invariant counts of real rational holomorphic curves were defined by Welschinger 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 of a potential approach of proving them. For many symplectic fourfolds and sixfolds, 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 (this is very different from Solomon's approach).