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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 14J17, 13C99, 14B05, 32B30

Retrieve articles in all journals with MSC: 14J17, 13C99, 14B05, 32B30

Additional Information

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