Maximal Cohen-Macaulay modules over the cone of an elliptic curve

Radu Laza; Gerhard Pfister; Dorin Popescu

doi:10.1016/S0021-8693(02)00052-2

Maximal Cohen-Macaulay modules over the cone of an elliptic curve

Radu Laza
, Gerhard Pfister
, Dorin Popescu

Mathematics

The University of Kaiserslautern-Landau
University of Bucharest

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

Let R = k[Y₁, Y₂, Y₃]/(f), f = Y₁ ³ + Y₂ ³ + Y₃ ³, where k is an algebraically closed field with char k ≠ 3. Using Atiyah bundle classification over elliptic curves we describe the matrix factorizations of the graded, indecomposable reflexive R-modules, equivalently we describe explicitly the indecomposable bundles over the projective curve V (f) ⊂ ℙ_k ². Using the fact that over the completion R̂ of R every reflexive module is gradable, we obtain a description of the maximal Cohen-Macaulay modules over R̂ = k[Y₁, Y₂, Y₃]/(f).

Original language	English
Pages (from-to)	209-236
Number of pages	28
Journal	Journal of Algebra
Volume	253
Issue number	2
DOIs	https://doi.org/10.1016/S0021-8693(02)00052-2
State	Published - Jul 15 2002

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title = "Maximal Cohen-Macaulay modules over the cone of an elliptic curve",

abstract = "Let R = k[Y1, Y2, Y3]/(f), f = Y1 3 + Y2 3 + Y3 3, where k is an algebraically closed field with char k ≠ 3. Using Atiyah bundle classification over elliptic curves we describe the matrix factorizations of the graded, indecomposable reflexive R-modules, equivalently we describe explicitly the indecomposable bundles over the projective curve V (f) ⊂ ℙk 2. Using the fact that over the completion {\^R} of R every reflexive module is gradable, we obtain a description of the maximal Cohen-Macaulay modules over {\^R} = k[Y1, Y2, Y3]/(f).",

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T1 - Maximal Cohen-Macaulay modules over the cone of an elliptic curve

AU - Laza, Radu

AU - Pfister, Gerhard

AU - Popescu, Dorin

PY - 2002/7/15

Y1 - 2002/7/15

N2 - Let R = k[Y1, Y2, Y3]/(f), f = Y1 3 + Y2 3 + Y3 3, where k is an algebraically closed field with char k ≠ 3. Using Atiyah bundle classification over elliptic curves we describe the matrix factorizations of the graded, indecomposable reflexive R-modules, equivalently we describe explicitly the indecomposable bundles over the projective curve V (f) ⊂ ℙk 2. Using the fact that over the completion R̂ of R every reflexive module is gradable, we obtain a description of the maximal Cohen-Macaulay modules over R̂ = k[Y1, Y2, Y3]/(f).

AB - Let R = k[Y1, Y2, Y3]/(f), f = Y1 3 + Y2 3 + Y3 3, where k is an algebraically closed field with char k ≠ 3. Using Atiyah bundle classification over elliptic curves we describe the matrix factorizations of the graded, indecomposable reflexive R-modules, equivalently we describe explicitly the indecomposable bundles over the projective curve V (f) ⊂ ℙk 2. Using the fact that over the completion R̂ of R every reflexive module is gradable, we obtain a description of the maximal Cohen-Macaulay modules over R̂ = k[Y1, Y2, Y3]/(f).

UR - https://www.scopus.com/pages/publications/0037101524

U2 - 10.1016/S0021-8693(02)00052-2

DO - 10.1016/S0021-8693(02)00052-2

M3 - Article

AN - SCOPUS:0037101524

SN - 0021-8693

VL - 253

SP - 209

EP - 236

JO - Journal of Algebra

JF - Journal of Algebra

IS - 2

ER -

Maximal Cohen-Macaulay modules over the cone of an elliptic curve

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