Universität zu Köln

Galinat, Lennart (2014). Orlov's equivalence and maximal Cohen-Macaulay modules over the cone of an elliptic curve. Math. Nachr., 287 (13). S. 1438 - 1456. WEINHEIM: WILEY-V C H VERLAG GMBH. ISSN 1522-2616

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Abstract

We describe a method for doing computations with Orlov's equivalence between the bounded derived category of certain hypersurfaces and the stable category of graded matrix factorisations of the polynomials describing these hypersurfaces. In the case of a smooth elliptic curve over an algebraically closed field we describe the indecomposable graded matrix factorisations of rank one. Since every indecomposable maximal Cohen-Macaulay module over the completion of a smooth cubic curve is gradable, we obtain explicit descriptions of all indecomposable rank one matrix factorisations of smooth cubic potentials. Finally, we explain how to compute all indecomposable matrix factorisations of higher rank with the help of a computer algebra system. (C) 2013 WILEY- VCHVerlag GmbH & Co. KGaA, Weinheim

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Galinat, Lennart UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-430208
DOI:	10.1002/mana.201300106
Journal or Publication Title:	Math. Nachr.
Volume:	287
Number:	13
Page Range:	S. 1438 - 1456
Date:	2014
Publisher:	WILEY-V C H VERLAG GMBH
Place of Publication:	WEINHEIM
ISSN:	1522-2616
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language CATEGORIES Multiple languages Mathematics Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/43020