TY - JOUR

T1 - On generators and relations of the rational cohomology of Hilbert schemes

AU - Bianchi, Andrea

AU - Christgau, Alexander Mangulad

AU - Pedersen, Jonathan Sejr

N1 - Publisher Copyright: © 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

PY - 2023

Y1 - 2023

N2 - 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).

AB - 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).

KW - Computational algebra

KW - Rational cohomology

KW - Symmetric groups

UR - http://www.scopus.com/inward/record.url?scp=85146897818&partnerID=8YFLogxK

U2 - 10.1007/s10801-022-01201-7

DO - 10.1007/s10801-022-01201-7

M3 - Journal article

AN - SCOPUS:85146897818

VL - 57

SP - 829

EP - 857

JO - Journal of Algebraic Combinatorics

JF - Journal of Algebraic Combinatorics

SN - 0925-9899

IS - 3

ER -