We exhibit a sharp Castelnuovo bound for the ith plurigenus of a smooth minimal surface of general type and of given degree d in the projective space , and classify the surfaces attaining the bound, at least when d⪢r. We give similar results for surfaces not necessarily minimal or of general type, but only for i⪢r (however, in the case r≤8, we give a complete classification, i.e., for any i≥1). In certain cases (only for r≥12) the surfaces with maximal plurigenus are not Castelnuovo surfaces, i.e., surfaces with maximal geometric genus.

DI GENNARO, V. (2001). A bound on the plurigenera of projective surfaces. JOURNAL OF PURE AND APPLIED ALGEBRA, 163(1), 69-79 [10.1016/S0022-4049(00)00131-6].

A bound on the plurigenera of projective surfaces

DI GENNARO, VINCENZO
2001

Abstract

We exhibit a sharp Castelnuovo bound for the ith plurigenus of a smooth minimal surface of general type and of given degree d in the projective space , and classify the surfaces attaining the bound, at least when d⪢r. We give similar results for surfaces not necessarily minimal or of general type, but only for i⪢r (however, in the case r≤8, we give a complete classification, i.e., for any i≥1). In certain cases (only for r≥12) the surfaces with maximal plurigenus are not Castelnuovo surfaces, i.e., surfaces with maximal geometric genus.
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/03 - Geometria
English
DI GENNARO, V. (2001). A bound on the plurigenera of projective surfaces. JOURNAL OF PURE AND APPLIED ALGEBRA, 163(1), 69-79 [10.1016/S0022-4049(00)00131-6].
DI GENNARO, V
Articolo su rivista
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/91020
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