Fourier-Mukai transform on Weierstrass cubics and commuting differential operators

Abstract

In this article, we describe the spectral sheaves of algebras of commuting differential operators of genus one and rank two with singular spectral curve, solving a problem posed by Previato and Wilson. We also classify all indecomposable semi-stable sheaves of slope one and ranks two or three on a cuspidal Weierstrass cubic.

References in corpus (1)

• Commuting ordinary differential operators with polynomial coefficients and automorphisms of the first Weyl algebra

Cited by in corpus (5)

• Commuting Ordinary Differential Operators and the Dixmier Test
• Cohen-Macaulay modules over the algebra of planar quasi-invariants and Calogero-Moser systems
• Schur-Sato theory for quasi-elliptic rings
• Centralizers of Rank One in the First Weyl Algebra
• On some questions around Berest's conjecture