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The Minimal Resolution Conjecture for Points on the Cubic Surface

Part of: Theory of modules and ideals Special varieties Commutative algebra: Homological methods

Published online by Cambridge University Press:  20 November 2018

M. Casanellas
M. Casanellas*
Affiliation:
DepartamentMatematica Aplicada I, ETSEIB UPC, Av. Diagonal 647, 08028-Barcelona. Spain, marta.casanellas@upc.edu
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Abstract

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In this paper we prove that a generalized version of the Minimal Resolution Conjecture given by Mustaţă holds for certain general sets of points on a smooth cubic surface $X\,\subset \,{{\mathbb{P}}^{3}}$. The main tool used is Gorenstein liaison theory and, more precisely, the relationship between the free resolutions of two linked schemes.

MSC classification

Primary: 13D02: Syzygies, resolutions, complexes
Secondary: 13C40: Linkage, complete intersections and determinantal ideals 14M05: Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) 14M07: Low codimension problems
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 61 , Issue 1 , 01 February 2009 , pp. 29 - 49
Copyright
Copyright © Canadian Mathematical Society 2009

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