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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Almost split sequences and Zariski differentials


Author: Alex Martsinkovsky
Journal: Trans. Amer. Math. Soc. 319 (1990), 285-307
MSC: Primary 14J17; Secondary 13C99, 14B05, 32B30
MathSciNet review: 955490
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Abstract: Let $ R$ be a complete two-dimensional integrally closed analytic $ k$-algebra. Associated with $ R$ is the Auslander module $ A$ from the fundamental sequence $ 0 \to {\omega _R} \to A \to R \to k \to 0$ and the module of Zariski differentials $ {D_k}{(R)^{ * * }}$. We conjecture that these modules are isomorphic if and only if $ R$ is graded. We prove this conjecture for (a) hypersurfaces $ f = X_3^n + {\text{g}}({X_1},{X_2})$, (b) quotient singularities, and (c) $ R$ graded Gorenstein.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1990-0955490-0
PII: S 0002-9947(1990)0955490-0
Keywords: Zariski differentials, Auslander module, almost split sequences, fundamental sequence, moduli algebra, matrix factorizations, graded analytic $ k$-algebras, reflexive modules, isolated hypersurface singularities
Article copyright: © Copyright 1990 American Mathematical Society