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Castelnuovo–Mumford regularity bounds for singular surfaces

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Abstract

We prove the regularity conjecture, namely Eisenbud–Goto conjecture, for a normal surface with rational, Gorenstein elliptic and log canonical singularities. Along the way, we bound the regularity for a dimension zero scheme by its Loewy length and for a curve allowing embedded or isolated point components by its arithmetic degree.

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Acknowledgments

Special thanks are due to professor Lawrence Ein for his generous help and encouragement. The author’s thanks also go to the referees for their nice comments and suggestions.

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  1. Department of Mathematics, Purdue University, West Lafayette, IN, 47907-2067, USA

    Wenbo Niu

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  1. Wenbo Niu
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Correspondence to Wenbo Niu.

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Niu, W. Castelnuovo–Mumford regularity bounds for singular surfaces. Math. Z. 280, 609–620 (2015). https://doi.org/10.1007/s00209-015-1439-2

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  • DOI: https://doi.org/10.1007/s00209-015-1439-2

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