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Projective normality and syzygies of algebraic surfaces

By Francisco Javier Gallego Rodrigo and Bangere 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: (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

Topics: Geometria algebraica
Publisher: Walter de Gruyter
Year: 2020
DOI identifier: 10.1515/crll.1999.506.145
OAI identifier: oai:www.ucm.es:15414
Provided by: EPrints Complutense

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