Renzo Cavalieri (Colorado State)
Tuesday, February 22, 2022 - 2:00pm
PDL C-38
Preseminar 2-2:30
Title: Chow rings and moduli spaces
Abstract: This talk will be an informal introduction to the notion of Chow rings, moduli spaces, and some basic ideas and techniques used in computing Chow rings of moduli spaces.
While I will have a general plabn of action for this talk, I also strongly encourage audience participation in guiding me through the material in such a way that the audience can draw the most benefits from the talk.
Seminar 2:30-3:30
Title: The integral Chow ring of \(M_{0}(\mathbb{P}^r,d)\)
Abstract: We give an efficient presentation of the Chow ring with integral coefficients of the open part of the moduli space of rational maps of odd degree to projective space. A less fancy description of this space has its closed points correspond to equivalence classes of \$(r+1)\$-tuples of degree \$d\$ polynomials in one variable with no common positive degree factor. We identify this space as a \$GL(2,\mathbb{C})\$ quotient of an open set in a projective space, and then obtain a (highly redundant) presentation by considering an envelope of the complement. A combinatorial analysis then leads us to eliminating a large number of relations, and to express the remaining ones in generating function form for all dimensions. The upshot of this work is to observe the rich combinatorial structure contained in the Chow rings of these moduli spaces as the degree and the target dimension vary. This is joint work with Damiano Fulghesu.
The talk will also be available via Zoom: https://washington.zoom.us/j/689897930
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