Euler characteristics of tautological bundles over Quot schemes of curves
Dragos Oprea, Shubham Sinha
TL;DR
This paper computes Euler characteristics of tautological bundles over Quot schemes of curves, providing explicit formulas for various cases including all genera and genus zero, advancing understanding of these geometric objects.
Contribution
It offers new closed-form formulas for Euler characteristics of tautological bundles over Quot schemes, including higher rank and symmetric powers, across different genera.
Findings
Closed-form expressions for Euler characteristics over punctual Quot schemes in all genera
Explicit results for higher rank quotients of trivial bundles in genus zero
Euler characteristics of symmetric powers of tautological bundles for rank zero quotients
Abstract
We compute the Euler characteristics of tautological vector bundles and their exterior powers over the Quot schemes of curves. We give closed-form expressions over punctual Quot schemes in all genera. For higher rank quotients of a trivial vector bundle, we obtain answers in genus zero. We also study the Euler characteristics of the symmetric powers of the tautological bundles, for rank zero quotients.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Alkaloids: synthesis and pharmacology · Tensor decomposition and applications