Projective normality and syzygies of algebraic surfaces
-
F. J Gallego
and
B. P Purnaprajna
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:
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,
effective bounds along the lines of Mukai's conjecture regarding projective normality and normal presentation for surfaces of positive Kodaira dimension, and,
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.
© Walter de Gruyter
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- Le problème de Brill-Noether pour des fibrés stables de petite pente
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- Bornes effectives pour la torsion des courbes elliptiques sur les corps de nombres
- Analytic functions on Zariski open sets, and local cohomology
- Projective normality and syzygies of algebraic surfaces
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Articles in the same Issue
- Le problème de Brill-Noether pour des fibrés stables de petite pente
- The affine curve-lengthening flow
- Bornes effectives pour la torsion des courbes elliptiques sur les corps de nombres
- Analytic functions on Zariski open sets, and local cohomology
- Projective normality and syzygies of algebraic surfaces
- The outer derivation of a complex Poisson manifold
- Nevanlinna-Pick interpolation on the bidisk
- The isoperimetric inequality for minimal surfaces in a Riemannian manifold
- Values of symmetric square L-functions at 1
