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The equations defining
blowup algebras of height three Gorenstein ideals
Andrew R. Kustin, Claudia Polini and Bernd Ulrich |
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Vol. 11 (2017), No. 7, 1489–1525
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Abstract |
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We find the defining equations of Rees rings of linearly presented height three Gorenstein ideals. To prove our main theorem we use local cohomology techniques to bound the maximum generator degree of the torsion submodule of symmetric powers in order to conclude that the defining equations of the Rees algebra and of the special fiber ring generate the same ideal in the symmetric algebra. We show that the ideal defining the special fiber ring is the unmixed part of the ideal generated by the maximal minors of a matrix of linear forms which is annihilated by a vector of indeterminates, and otherwise has maximal possible height. An important step in the proof is the calculation of the degree of the variety parametrized by the forms generating the height three Gorenstein ideal. |
Keywords
blowup algebra, Castelnuovo–Mumford regularity, degree of a
variety, Hilbert series, ideal of linear type, Jacobian
dual, local cohomology, morphism, multiplicity, Rees ring,
residual intersection, special fiber ring
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Mathematical Subject Classification 2010
Primary: 13A30
Secondary: 13D02, 13D45, 13H15, 14A10, 14E05
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Milestones
Received: 19 June 2015
Revised: 17 October 2016
Accepted: 19 December 2016
Published: 7 September 2017
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Authors |
| Andrew R. Kustin | |
| Department of Mathematics University of South Carolina 1523 Greene Street Columbia, SC 29208 United States |
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| Claudia Polini | |
| Department of Mathematics University of Notre Dame 255 Hurley Hall Notre Dame, IN 46556-4618 United States |
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| Bernd Ulrich | |
| Department of Mathematics Purdue University 150 N University Street West Lafayette, IN 47907-2067 United States |
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