Starts 25 Jan 2023 19:00
Ends 25 Jan 2023 20:00
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Algebraic Geometry Seminar: Tautological bundles over Quot schemes on curves
Online
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https://zoom.us/meeting/register/tJEpcuqrqDIqHdcVyFUZsc2H20ws-sACSEZ4
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Abstract: I will present formulas for the Euler characteristics of tautological bundles over punctual Quot schemes that parameterize zero-dimensional quotients of a vector bundle E over C (based on joint work with Prof. Dragos Oprea). The formulas suggest analogies between the Quot schemes of curves and the Hilbert scheme of points of surfaces. Our proofs rely on Atiyah-Bott localization, universality results (of Ellingsrud, Göttsche, and Lehn), and the combinatorics of Schur functions. For higher rank quotients, I will report a few formulas and vanishing results when the genus is zero.
https://zoom.us/meeting/register/tJEpcuqrqDIqHdcVyFUZsc2H20ws-sACSEZ4
After registering, you will receive a confirmation email containing information about joining the meeting.
Abstract: I will present formulas for the Euler characteristics of tautological bundles over punctual Quot schemes that parameterize zero-dimensional quotients of a vector bundle E over C (based on joint work with Prof. Dragos Oprea). The formulas suggest analogies between the Quot schemes of curves and the Hilbert scheme of points of surfaces. Our proofs rely on Atiyah-Bott localization, universality results (of Ellingsrud, Göttsche, and Lehn), and the combinatorics of Schur functions. For higher rank quotients, I will report a few formulas and vanishing results when the genus is zero.