Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



Kustin-Miller unprojection with complexes

Author: Stavros Argyrios Papadakis
Journal: J. Algebraic Geom. 13 (2004), 249-268
Published electronically: October 15, 2003
MathSciNet review: 2047698
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Abstract | References | Additional Information

Abstract: A main ingredient for the Kustin-Miller unprojection is the module $\operatorname{Hom}_R(I, \omega_R)$, where $R$ is a local Gorenstein ring and $I$ a codimension one ideal with $R/I$ Gorenstein. We prove a method of calculating it in a relative setting using resolutions. We give three applications. In the first we generalise a result of Catanese, Franciosi, Hulek, and Reid (Embeddings of curves and surfaces, Nagoya Math. J. 154 (1999), 185-220). The second and the third are about Tom and Jerry, two families of Gorenstein codimension four rings with $9 \times 16$ resolutions.

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Additional Information

Stavros Argyrios Papadakis
Affiliation: Math Institute, University of Warwick, Coventry CV4 7AL, England
Address at time of publication: Fakultät für Mathematik und Informatik, Geb. 27, Universität des Saarlandes, D-66123 Saarbrücken, Gernamy

Received by editor(s): August 24, 2001
Published electronically: October 15, 2003
Additional Notes: This work is part of a Warwick Ph.D. thesis \cite{P}, financially supported by the Greek State Scholarships Foundation