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The commuting scheme and generic pipe dreams
Algebraic Geometry and Number Theory| Speaker: | Allen Knutson, Cornell University |
| Related Webpage: | https://math.cornell.edu/allen-knutson |
| Location: | 1147 MSB |
| Start time: | Tue, Nov 30 2021, 11:00AM |
The space of pairs of commuting matrices is more mysterious than you might think -- in particular, Hochster's 1984 conjecture that it is reduced remains unresolved. I'll explain how to degenerate it to one component of the "lower-upper scheme" {(X,Y) : XY lower triangular, YX upper triangular}, a reduced complete intersection, and how to compute the degree of any component as a sum over "generic pipe dreams". As a consequence, this recovers both the "pipe dream" and "bumpless pipe dream" formulae for double Schubert polynomials. Some of this work is joint with Paul Zinn-Justin.