Universally counting curves in Calabi--Yau threefolds
Organizers
Speaker
John Pardon
Time
Thursday, April 16, 2026 9:15 AM - 10:15 AM
Venue
A6-101
Online
Zoom 638 227 8222
(BIMSA)
Abstract
Generic transversality for pseudo-holomorphic curves in almost complex manifolds is usually regarded as a technical fact used in the foundations of the enumerative theory of pseudo-holomorphic curves. On the other hand, the proof of the Gopakumar--Vafa integrality conjecture by Ionel--Parker used generic transversality as a crucial ingredient, to reduce it to the case of local curves. I will discuss how to transport this sort of generic transversality argument to the considerably more rigid setting of complex analytic geometry. We then use it to show that curve enumeration invariants for semi-Fano threefolds are determined by their values on local curves. This implies the MNOP conjecture for such threefolds and primary insertions (as it is known for local curves by work of Bryan--Pandharipande and Okounkov--Pandharipande).