On higher syzygies of ruled surfaces

Author:
Euisung Park

Journal:
Trans. Amer. Math. Soc. **358** (2006), 3733-3749

MSC (2000):
Primary 13D02, 14J26, 14N05

DOI:
https://doi.org/10.1090/S0002-9947-05-03875-4

Published electronically:
December 27, 2005

MathSciNet review:
2218997

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Abstract | References | Similar Articles | Additional Information

Abstract: We study higher syzygies of a ruled surface over a curve of genus with the numerical invariant . Let Pic be a line bundle in the numerical class of . We prove that for , satisfies property if and , and for , satisfies property if and . By using these facts, we obtain Mukai-type results. For ample line bundles , we show that satisfies property when and or when and . Therefore we prove Mukai's conjecture for ruled surface with . We also prove that when is an elliptic ruled surface with , satisfies property if and only if and .

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Additional Information

**Euisung Park**

Affiliation:
School of Mathematics, Korea Institute for Advanced Study, 207-43 Cheongryangri 2-dong, Dongdaemun-gu, Seoul 130-722, Republic of Korea

Email:
puserdos@kias.re.kr

DOI:
https://doi.org/10.1090/S0002-9947-05-03875-4

Received by editor(s):
January 26, 2004

Received by editor(s) in revised form:
October 16, 2004

Published electronically:
December 27, 2005

Additional Notes:
The author was supported by Korea Research Foundation Grant (KRF-2002-070-C00003).

Article copyright:
© Copyright 2005
American Mathematical Society