Divisors on Mg,g+1 and the minimal resolution conjecture for points on canonical curves

Gavril Farkas; Mircea Musţǎ; Mihnea Popa

doi:10.1016/S0012-9593(03)00022-3

Divisors on M_g,g+1 and the minimal resolution conjecture for points on canonical curves

Gavril Farkas^*, Mircea Musţǎ, Mihnea Popa

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

27 Scopus citations

Abstract

We use geometrically defined divisors on moduli spaces of pointed curves to compute the graded Betti numbers of general sets of points on any nonhyperelliptic canonically embedded curve. This gives a positive answer to the Minimal Resolution Conjecture in the case of canonical curves. But we prove that the conjecture fails on curves of large degree. These results are related to the existence of theta divisors associated to certain stable vector bundles.

Original language	English (US)
Pages (from-to)	553-581
Number of pages	29
Journal	Annales Scientifiques de l'Ecole Normale Superieure
Volume	36
Issue number	4
DOIs	https://doi.org/10.1016/S0012-9593(03)00022-3
State	Published - Jul 2003

ASJC Scopus subject areas

General Mathematics

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10.1016/S0012-9593(03)00022-3

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abstract = "We use geometrically defined divisors on moduli spaces of pointed curves to compute the graded Betti numbers of general sets of points on any nonhyperelliptic canonically embedded curve. This gives a positive answer to the Minimal Resolution Conjecture in the case of canonical curves. But we prove that the conjecture fails on curves of large degree. These results are related to the existence of theta divisors associated to certain stable vector bundles.",

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AB - We use geometrically defined divisors on moduli spaces of pointed curves to compute the graded Betti numbers of general sets of points on any nonhyperelliptic canonically embedded curve. This gives a positive answer to the Minimal Resolution Conjecture in the case of canonical curves. But we prove that the conjecture fails on curves of large degree. These results are related to the existence of theta divisors associated to certain stable vector bundles.

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Divisors on M_g,g+1 and the minimal resolution conjecture for points on canonical curves

Abstract

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