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\centerline{\bf Cohen-Macaulay representation on cubic surfaces}
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\centerline{Dorin Popescu}
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Let $R=k[Y_1,Y_2,Y_3]/(f)$
$f=Y_1^3+Y_2^3+Y_3^3$, where $k$ is an algebraically closed field with
char $k\not=3$. Using Atiyah bundles classification over elliptic curves we
describe the matrix factorizations of the graded, indecomposable reflexive
$R$-modules. This classification depends on three parameters, two discrete
parameters (one is the rank) and a continuous one - the points of the curve
$V(f)\subset {\bf P}_k^2$.
We write canonical normal forms for the matrix factorizations of all
graded reflexive $R$-modules of rank one and show effectively how we can
produce the indecomposable graded reflexive $R$-modules of ranks $\geq 2$
using SINGULAR with help of a computer.
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