On Generators and Relations of the Rational Cohomology of Hilbert Schemes
Andrea Bianchi, Alexander Mangulad Christgau, Jonathan Sejr, Pedersen

TL;DR
This paper studies the algebraic structure of the rational cohomology of Hilbert schemes of points on the complex plane, identifying minimal generators and relations, and exploring their degrees and conjectures for general cases.
Contribution
It determines minimal generators and relations for the cohomology algebra of Hilbert schemes, providing new insights into their algebraic structure and related moduli spaces.
Findings
Identified two minimal sets of generators for the algebra
Determined degrees at which relations first occur
Proposed conjectures for the structure of relations for all d
Abstract
We consider for the graded commutative -algebra , which is also connected to the study of generalised Hurwitz spaces by work of the first author. These Hurwitz spaces are in turn related to the moduli spaces of Riemann surfaces with boundary. We determine two distinct, minimal sets of multiplicative generators of . Additionally, we prove when the lowest degree generating relations occur. For small values of we also determine a minimal set of generating relations, which leads to several conjectures about the necessary generating relations for .
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Taxonomy
TopicsPolynomial and algebraic computation · Commutative Algebra and Its Applications · Advanced Differential Equations and Dynamical Systems
