The Konno invariant of some algebraic varieties

Lawrence Ein; Robert Lazarsfeld

doi:10.1007/s40879-019-00322-x

The Konno invariant of some algebraic varieties

Lawrence Ein
, Robert Lazarsfeld

Mathematics

University of Illinois at Chicago

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

3 Scopus citations

Abstract

The Konno invariant of a projective variety X is the minimum geometric genus of the fiber of a rational pencil on X. It was computed by Konno for surfaces in P³, and in general can be viewed as a measure of the complexity of X. We estimate Konno (X) for some natural classes of varieties, including sharp asymptotics for polarized K3 surfaces. In an appendix, we give a quick proof of a classical formula due to Deligne and Hoskin for the colength of an integrally closed ideal on a surface.

Original language	English
Pages (from-to)	420-429
Number of pages	10
Journal	European Journal of Mathematics
Volume	6
Issue number	2
DOIs	https://doi.org/10.1007/s40879-019-00322-x
State	Published - Jun 1 2020

Keywords

Algebraic variety
Fibration
Geometric genus
Multiplicity of linear series on surface

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abstract = "The Konno invariant of a projective variety X is the minimum geometric genus of the fiber of a rational pencil on X. It was computed by Konno for surfaces in P3, and in general can be viewed as a measure of the complexity of X. We estimate Konno (X) for some natural classes of varieties, including sharp asymptotics for polarized K3 surfaces. In an appendix, we give a quick proof of a classical formula due to Deligne and Hoskin for the colength of an integrally closed ideal on a surface.",

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AB - The Konno invariant of a projective variety X is the minimum geometric genus of the fiber of a rational pencil on X. It was computed by Konno for surfaces in P3, and in general can be viewed as a measure of the complexity of X. We estimate Konno (X) for some natural classes of varieties, including sharp asymptotics for polarized K3 surfaces. In an appendix, we give a quick proof of a classical formula due to Deligne and Hoskin for the colength of an integrally closed ideal on a surface.

KW - Algebraic variety

KW - Fibration

KW - Geometric genus

KW - Multiplicity of linear series on surface

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JF - European Journal of Mathematics

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ER -

The Konno invariant of some algebraic varieties

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Keywords

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