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Quotients of abelian varieties by reflection groups
Eric M. Rains
We prove (by a case-by-case analysis) a conjecture of Bernstein/Schwarzman to the effect that quotients of abelian varieties by suitable actions of (complex) reflection groups are…
Filtered deformations of elliptic algebras
Eric M. Rains
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…
The birational geometry of noncommutative surfaces
Eric M. Rains
We show that any commutative rationally ruled surface with a choice of anticanonical curve admits a 1-parameter family of noncommutative deformations parametrized by the Jacobian o…
Hyperelliptic limits of quadrics through canonical curves and ribbons
Alexander Polishchuk, Eric Rains
We describe explicitly all hyperelliptic limits of quadrics through smooth canonical curves of genus in . Also, we construct an open embedding of the blow up…
Elliptic Double Affine Hecke Algebras
Eric M. Rains
We give a construction of an affine Hecke algebra associated to any Coxeter group acting on an abelian variety by reflections; in the case of an affine Weyl group, the result is an…
Invariant theory of and genus 2 curves
Eric M. Rains, Steven V Sam
Previous work established a connection between the geometric invariant theory of the third exterior power of a 9-dimensional complex vector space and the moduli space of genus 2 cu…