##### Department of Mathematics,

University of California San Diego

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### Math 208 - Algebraic Geometry Seminar

## Sergej Monavari

#### Utrecht University

## Double nested Hilbert schemes and stable pair invariants

##### Abstract:

Hilbert schemes of points on a smooth projective curve are simply symmetric powers of the curve itself; they are smooth and we know essentially everything about them. We propose a variation by studying double nested Hilbert schemes of points, which parametrize flags of 0-dimensional subschemes satisfying certain nesting conditions dictated by Young diagrams. These moduli spaces are almost never smooth but admit a virtual structure à la Behrend-Fantechi. We explain how this virtual structure plays a key role in (re)proving the correspondence between Gromov-Witten invariants and stable pair invariants for local curves, and say something on their K-theoretic refinement.

Host: Dragos Oprea

### January 28, 2022

### 10:30 AM

Pre-talk at 10:00 AM

Contact Samir Canning (srcannin@ucsd.edu) for zoom access.

Research Areas

Algebraic Geometry****************************