Quantum Lefschetz theorem revisited
Time: 2021-01-08
Published By: Kangkang Deng
Speaker(s): Jun Wang
Time: 15:00-16:00 January 8, 2021
Venue: Room 29, Quan Zhai, BICMR
Abstract: Gromov-Witten(GW) theory is a modern curve-counting theory. A natural question in GW theory is to study the relationship of (virtual )number of curves (known as GW invariants) in an ambient space and (virtual) number of curves of its complete intersection. In genus zero, this is usually done by the quantum Lefschetz principle, which relates the twisted GW invariants of the ambient space to GW invariants of its complete intersection. But this approach needs a technical condition called convexity. When the convexity fails, the recent progress of quasimap wall-crossing theorem helps us to remove the convexity condition, but we require the ambient space belongs to the class of GIT targets , which includes toric orbifolds, flag varieties. We will discuss a ongoing quantum Lefschetz theorem for which the ambient space is a non-GIT target and the convexity condition may fail. If time permits, we will discuss some applications of quantum Lefschetz theorem to other question in Gromov-Witten theory.
