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1 April 2002 Exterior algebra methods for the minimal resolution conjecture
David Eisenbud, Sorin Popescu, Frank-Olaf Schreyer, Charles Walter
Duke Math. J. 112(2): 379-395 (1 April 2002). DOI: 10.1215/S0012-9074-02-11226-5

Abstract

If $r\geq 6,r\neq 9$, we show that the minimal resolution conjecture (MRC) fails for a general set of $\gamma$ points in $\mathbb {P}\sp r$ for almost $(1/2)\sqrt {r}$ values of $\gamma$. This strengthens the result of D. Eisenbud and S. Popescu [EP1], who found a unique such $\gamma$ for each $r$ in the given range. Our proof begins like a variation of that of Eisenbud and Popescu, but uses exterior algebra methods as explained by Eisenbud, G. Fløystad, and F.- O. Schreyer [EFS] to avoid the degeneration arguments that were the most difficult part of the Eisenbud-Popescu proof. Analogous techniques show that the MRC fails for linearly normal curves of degree $d$ and genus $g$ when $d\geq 3g-2,g\geq 4$, re-proving results of Schreyer, M. Green, and R. Lazarsfeld.

Citation

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David Eisenbud. Sorin Popescu. Frank-Olaf Schreyer. Charles Walter. "Exterior algebra methods for the minimal resolution conjecture." Duke Math. J. 112 (2) 379 - 395, 1 April 2002. https://doi.org/10.1215/S0012-9074-02-11226-5

Information

Published: 1 April 2002
First available in Project Euclid: 18 June 2004

zbMATH: 1035.13008
MathSciNet: MR1894365
Digital Object Identifier: 10.1215/S0012-9074-02-11226-5

Subjects:
Primary: 13D02
Secondary: 14M05, 15A75

Rights: Copyright © 2002 Duke University Press

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Vol.112 • No. 2 • 1 April 2002
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