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Author: Burban, Igor × End date: 2019 × Start date: 2019 × End date: 2016 × Start date: 2010 × Type: Text × Publisher: Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach ×

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    Fourier-Mukai transform on Weierstrass cubics and commuting cifferential operators
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2016) Burban, Igor; Zheglov, Alexander
    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.
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    Maximal Cohen-Macaulay modules over non-isolated surface singularities and matrix problems
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2015) Burban, Igor; Drozd, Yuriy
    In this article we develop a new method to deal with maximal Cohen{ Macaulay modules over non{isolated surface singularities. In particular, we give a negative answer on an old question of Schreyer about surface singularities with only countably many indecomposable maximal Cohen{Macaulay modules. Next, we prove that the degenerate cusp singularities have tame Cohen{Macaulay representation type. Our approach is illustrated on the case of kJx; y; zK=(xyz) as well as several other rings. This study of maximal Cohen{Macaulay modules over non{isolated singularities leads to a new class of problems of linear algebra, which we call representations of decorated bunches of chains. We prove that these matrix problems have tame representation type and describe the underlying canonical forms.