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Let $E$ be an elliptic curve. When the symmetric group $Sigma_{g+1}$ of order $(g+1)!$ acts on $E^{g+1}$ in the natural way, the subgroup $E_0^{g+1}$, consisting of those $(g+1)$-tuples whose coordinates sum to zero, is stable under the action of $Sigma_{g+1}$. It is isomorphic to $E^g$. This paper concerns the structure of the quotient variety $E^g/Sigma$ when $Sigma$ is a subgroup of $Sigma_{g+1}$ generated by simple transpositions. In an earlier paper we observed that $E^g/Sigma$ is a bundle over a suitable power, $E^N$, with fibers that are products of projective spaces. This paper shows that $E^g/Sigma$ has an etale cover by a product of copies of $E$ and projective spaces with an abelian Galois group.
The elliptic algebras in the title are connected graded $mathbb{C}$-algebras, denoted $Q_{n,k}(E,tau)$, depending on a pair of relatively prime integers $n>kge 1$, an elliptic curve $E$, and a point $tauin E$. This paper examines a canonical homomorp
In this paper we describe the category of motives for an elliptic curve in the sense of Voevodsky as a derived category of dg modules over a commutative differential graded algebra in the category of representations over some reductive group.
One of the difficulties in doing noncommutative projective geometry via explicitly presented graded algebras is that it is usually quite difficult to show flatness, as the Hilbert series is uncomputable in general. If the algebra has a regular centra
This note studies the existence of quotients by finite set theoretic equivalence relations. May 18: Substantial revisions with a new appendix by C. Raicu
We compute the Hodge polynomials for the moduli space of representations of an elliptic curve with two marked points into SL(2,C). When we fix the conjugacy classes of the representations around the marked points to be diagonal and of modulus one, th