Bounds for the cohomology and the Castelnuovo regularity of certain surfaces

Brodmann, M; Vogel, W (1993). Bounds for the cohomology and the Castelnuovo regularity of certain surfaces. Nagoya Mathematical Journal, 131:109-126.

Abstract

We bound the cohomology and the Castelnuovo-Mumford regularity of normal projective surfaces with smooth rational generic hyperplane section in terms of their embedding dimension, their degree and their Buchsbaum order. In particular we show that for arbitrary 2-Buchsbaum surfaces a question of D. Eisenbud about Castelnuovo-Mumford regularity has a positive answer.

Abstract

We bound the cohomology and the Castelnuovo-Mumford regularity of normal projective surfaces with smooth rational generic hyperplane section in terms of their embedding dimension, their degree and their Buchsbaum order. In particular we show that for arbitrary 2-Buchsbaum surfaces a question of D. Eisenbud about Castelnuovo-Mumford regularity has a positive answer.

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