The Frobenius Characteristic of the Orlik-Terao Algebra of Type A

We provide a new virtual description of the symmetric group action on the cohomology of ordered configuration space on SU2 up to translations. We use this formula to prove the Moseley-Proudfoot-Young conjecture. As a consequence we obtain the graded Frobenius character of the Orlik-Terao algebra of type An

On the cohomology of arrangements of subtori

Given an arrangement of subtori of arbitrary codimension in a complex torus, we compute the cohomology groups of the complement. Then, by using the Leray spectral sequence, we describe the multiplicative structure on the associated graded cohomology. We also provide a differential model for the cohomology ring, by considering a toric wonderful model and its Morgan algebra. Finally, we focus on the divisorial case, proving a new presentation for the cohomology of toric arrangements

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

We construct a differential graded algebra to compute the cohomology of ordered configuration spaces on an algebraic variety with vanishing Euler characteristic. We show that the k-th Betti number of Conf (C, n) (C is an elliptic curve) grows as a polynomial of degree exactly 2 k- 2. We also compute [InlineEquation not available: see fulltext.] for k< 6 and arbitrary n

Poincar\ue9 polynomial of elliptic arrangements is not determined by the Tutte polynomial

The Poincar\ue9 polynomial of the complement of an arrangement in a non compact group G is a specialization of the G-Tutte polynomial associated with the arrangement. In this article we show two unimodular elliptic arrangements (built up from two graphs) with the same Tutte polynomial, having different Betti numbers

Orientable arithmetic matroids

The theory of matroids has been generalized to oriented matroids and, recently, to arithmetic matroids. We want to give a definition of \u201coriented arithmetic matroid\u201d and prove some properties like the \u201cuniqueness of orientation\u201d

Hodge Theory for Polymatroids

We construct a Leray model for a discrete polymatroid with arbitrary building set and we prove a generalized Goresky-MacPherson formula. The first row of the model is the Chow ring of the polymatroid; we prove Poincare duality, Hard Lefschetz, and Hodge-Riemann theorems for the Chow ring. Furthermore, we provide a relative Lefschetz decomposition with respect to the deletion of an element

Corrigendum: Orlik-Solomon-type presentations for the cohomology algebra of toric arrangements

In this short note we correct the statement of the main result of [Trans. Amer. Math. Soc. 373 (2020), no. 3, 1909-1940]. That paper presented the rational cohomology ring of a toric arrangement by generators and relations. One of the series of relations given in the paper is indexed over the set circuits in the arrangement's arithmetic matroid. That series of relations should however be indexed over all sets X with |X| = rk(X) + 1. Below we give the complete and correct presentation of the rational cohomology ring