Asymptotic growth of Betti numbers of ordered configuration spaces on an elliptic curve

Abstract

We construct a dga to computing the cohomology of ordered configuration spaces on an algebraic variety with vanishing Euler characteristic. It follows that the $k$-th Betti number of $Conf(C,n)$ ($C$ is an elliptic curve) grows as a polynomial of degree exactly $2k-2$. We also compute $H^k(Conf(C,n))$ for $k\le 5$ and arbitrary $n$.

16 pages, 11 tables

References in corpus (3)

• Gröbner methods for representations of combinatorial categories
• The connection between combinatorics and cohomology of elliptic arrangements
• The cohomology rings of the unordered configuration spaces of the torus

Cited by in corpus (2)

• Secondary representation stability and the ordered configuration space of the once-punctured torus
• Extra structure on the cohomology of configuration spaces of closed orientable surfaces