A bound on the plurigenera of projective surfaces

✍ Scribed by Vincenzo Di Gennaro

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 101 KB
• Volume: 163
• Category: Article
• ISSN: 0022-4049
• DOI: 10.1016/s0022-4049(00)00131-6

✦ Synopsis

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 P r , and classify the surfaces attaining the bound, at least when dr. We give similar results for surfaces not necessarily minimal or of general type, but only for ir (however, in the case r ≤ 8, we give a complete classiÿcation, 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.