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Projective normality and higher syzygies for algebraic surfaces
Gallego, Francisco Javier Purnaprajna, Bangere P.
Gallego, Francisco Javier
Purnaprajna, Bangere P.
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Abstract
In this work we develop new techniques to compute Koszul cohomology
groups for several classes of varieties. As applications we prove results on projective
normality and syzygies for algebraic surfaces. From more general results we obtain in
particular the following:
(a) Mukai's conjecture (and stronger variants of it) regarding projective normality
and normal presentation for surfaces with Kodaira dimension 0, and uniform bounds for
higher syzygies associated to adjoint linear series,
(b) effective bounds along the lines of Mukai's conjecture regarding projective normality
and normal presentation for surfaces of positive Kodaira dimension, and,
(c) results on projective normality for pluricanonical models of surfaces of general
type (recovering and strengthening results by Ciliberto) and generalizations of them to
higher syzygies.
In addition, we also extend the above results to singular surfaces.
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This is the published version.
Date
1999-03-05
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De Gruyter Open
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Gallego, F. J. & Purnaprajna, B. P. "Projective normality and higher syzygies for algebraic surfaces." Journal fur die reine und angewandte Mathematik. Vol 506. pp. 145-180.