Evolution equation in Hilbert-Mumford calculus
Ziv Ran
TL;DR
This paper introduces an evolution equation that captures the intersection theory of tautological classes on the Hilbert scheme of a family of nodal curves, linking differential equations with algebraic geometry.
Contribution
It formulates an evolution-type differential equation that encodes intersection theory on Hilbert schemes of nodal curves, providing a new analytical approach.
Findings
Derived the evolution equation for tautological classes
Connected differential equations with intersection theory
Provided a framework for analyzing Hilbert schemes
Abstract
An evolution-type differential equation encodes the intersection theory of tautological classes on the Hilbert scheme of a family of nodal curves.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Nonlinear Waves and Solitons · Polynomial and algebraic computation