Kustin–Miller unprojection with complexes
Author:
Stavros Argyrios Papadakis
Journal:
J. Algebraic Geom. 13 (2004), 249268
DOI:
https://doi.org/10.1090/S1056391103003503
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, D66123 Saarbrücken, Gernamy
Email:
spapad@maths.warwick.ac.uk, papadakis@math.unisb.de
Received by editor(s):
August 24, 2001
Published electronically:
October 15, 2003
Additional Notes:
This work is part of a Warwick Ph.D. thesis [Gorenstein rings and Kustin–Miller unprojection, Univ. of Warwick Ph.D. thesis, Aug 2001], financially supported by the Greek State Scholarships Foundation