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Projective normality and syzygies of algebraic surfaces

Gallego Rodrigo, Francisco Javier and Purnaprajna, Bangere P. (1999) Projective normality and syzygies of algebraic surfaces. Journal für die reine und angewandte Mathematik, 506 . pp. 145-180. ISSN 0075-4102

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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.

Item Type:Article
Additional Information:Erratum ibid. 523, 233-234 (2000)
Uncontrolled Keywords:Koszul cohomology; Projective normality; Syzygies; Enriques surfaces; Adjoint bundles; surfaces of general type
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:15414
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