On generators and relations of the rational cohomology of Hilbert schemes
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We consider for d≥ 1 the graded commutative Q-algebra A(d) : = H∗(Hilb d(C2) ; Q) , 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 ⌊ d/ 2 ⌋ multiplicative generators of A(d). Additionally, we prove when the lowest degree generating relations occur. For small values of d, we also determine a minimal set of generating relations, which leads to several conjectures about the necessary generating relations for A(d).
Original language | English |
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Journal | Journal of Algebraic Combinatorics |
Volume | 57 |
Issue number | 3 |
Pages (from-to) | 829-857 |
Number of pages | 29 |
ISSN | 0925-9899 |
DOIs | |
Publication status | Published - 2023 |
Bibliographical note
Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
- Computational algebra, Rational cohomology, Symmetric groups
Research areas
ID: 336292357