Apr 25, 2024
Shifted Lagrange multipliers method
Algebraic Geometry and Number Theory Seminar
Date: April 25, 2024 |
1:00 pm –
Speaker: Young-Hoon Kiem, KIAS, Seoul
Location: Heinzel Seminar Room (I21.EG.101), Office Building West, ISTA
Modern enumerative geometry is about integrals of cohomology classes against virtual fundamental classes of moduli spaces. When the perfect obstruction theory of a moduli space admits a cosection, the virtual fundamental class is localized to the zero locus of the cosection. When the cosection can be enhanced to a (-1)-shifted closed 1-form, the zero locus admits a (-2)-shifted symplectic structure and hence a virtual fundamental class due to a recent construction of Oh-Thomas. I will talk about a joint work with Hyeonjun Park where we prove that the two virtual fundamental classes coincide up to sign. When applied to a shifted form of Lagrange multipliers method, the result gives us an immediate proof of the quantum Lefschetz principle by Chang-Li.