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Exterior algebra methods for the minimal resolution conjecture
David Eisenbud, Sorin Popescu, Frank-Olaf Schreyer, and Charles Walter
Source: Duke Math. J. Volume 112, Number 2
(2002), 379-395.
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.
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.dmj/1087575156
Mathematical Reviews number (MathSciNet): MR1894365
Digital Object Identifier: doi:10.1215/S0012-9074-02-11226-5
Zentralblatt MATH identifier: 1035.13008
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