On manifolds swept out by high dimensional hypersurfaces

Taku Suzuki

doi:10.1016/j.jpaa.2015.05.021

On manifolds swept out by high dimensional hypersurfaces

Taku Suzuki

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we prove that, if an embedded smooth projective manifold is swept out by high dimensional hypersurfaces of degree d, then either it is a scroll, or it admits an extremal contraction whose general fibers are hypersurfaces of degree d, under the assumption of Hartshorne's famous conjecture on complete intersections.

Original language	English
Pages (from-to)	5394-5401
Number of pages	8
Journal	Journal of Pure and Applied Algebra
Volume	219
Issue number	12
DOIs	https://doi.org/10.1016/j.jpaa.2015.05.021
Publication status	Published - 2015 Dec 1

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jpaa.2015.05.021

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abstract = "In this paper, we prove that, if an embedded smooth projective manifold is swept out by high dimensional hypersurfaces of degree d, then either it is a scroll, or it admits an extremal contraction whose general fibers are hypersurfaces of degree d, under the assumption of Hartshorne's famous conjecture on complete intersections.",

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