2011
DOI: 10.1016/j.jpaa.2010.10.009
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Minimal free resolutions of general points lying on cubic surfaces in P3

Abstract: a b s t r a c tCasanellas has shown that a generalized version of Lorenzini's Minimal Resolution Conjecture (as modified by Mustaţǎ) holds for a set of t general points on a smooth cubic surface in P 3 , for certain specific values of t. We extend her work by verifying the conjecture for all t, and by allowing the cubic surface to have isolated double points.

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Cited by 8 publications
(1 citation statement)
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References 17 publications
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“…For example, if one has a graded Cohen–Macaulay -algebra, then one can take a quotient by generic linear forms to produce an Artinian ring. A reduction of this kind is called an Artinian reduction and provides many useful tools to work with, and almost all homological invariants of the ring are preserved [18]. Unfortunately, we will not be able to use these tools or reductions as the coordinate ring of a generic collection of lines is almost never Cohen–Macaulay, whereas the coordinate ring of a generic collection of points is always Cohen–Macaulay.…”
Section: Introductionmentioning
confidence: 99%
“…For example, if one has a graded Cohen–Macaulay -algebra, then one can take a quotient by generic linear forms to produce an Artinian ring. A reduction of this kind is called an Artinian reduction and provides many useful tools to work with, and almost all homological invariants of the ring are preserved [18]. Unfortunately, we will not be able to use these tools or reductions as the coordinate ring of a generic collection of lines is almost never Cohen–Macaulay, whereas the coordinate ring of a generic collection of points is always Cohen–Macaulay.…”
Section: Introductionmentioning
confidence: 99%