Exterior algebra methods for the Minimal Resolution Conjecture

Details Exterior algebra methods for the Minimal Resolution Conjecture Exterior algebra methods for the Minimal Resolution Conjecture

2000-11-28

arxiv.org/abs/math/0011236v1

Mathematics

Algebraic Geometry

15 pages, Plain TeX, uses diagrams.tex

Scientific paper

If r\geq 6, r\neq 9, we show that the Minimal Resolution Conjecture fails for a general set of m points in P^r for almost 1/2\sqrt r values of m. This strengthens the result of Eisenbud and Popescu [1999], who found a unique such m 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 and Schreyer [2000] to avoid the degeneration arguments that were the most difficult part of the Eisenbud-Popescu proof. Analogous techniques show that the Minimal Resolution Conjecture fails for linearly normal curves of degree d and genus g when d\geq 3g-2, g\geq 4, reproving results of Schreyer, Green, and Lazarsfeld.

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