Multiplicative structure of the K-theoretic McKay correspondence for Hilbert scheme of points
- Prelegent(ci)
- Jakub Koncki
- Afiliacja
- IMPAN/UW
- Termin
- 8 stycznia 2024 10:30
- Pokój
- p. 4070
- Seminarium
- Seminarium „Topologia algebraiczna”
Hilbert scheme of points in a complex plane is a classical object of study in algebraic geometry. McKay correspondence provides an isomorphism of vector spaces between its K-theory (or cohomology) and the space of symmetric functions, creating a bridge between geometry and combinatorics. Multiplication by a class in the K-theory induces an endomorphism of the space of symmetric functions.
In the cohomology case, compact formulas for such maps were found by Lehn and Sorger. The K-theoretical case was studied by Boissière using torus equivariant techniques. He proved a formula for multiplication by the class of tautological bundle and stated a conjecture for remaining generators of the K-theory of Hilbert scheme. In the talk I will show how torus action simplifies the problem and prove the conjectured formula using restriction to a one-dimensional subtorus.
This is a joint project with M. Zielenkiewicz.