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arXiv · 1808.04331

The Konno invariant of some algebraic varieties

Lawrence Ein·Robert Lazarsfeld
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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 P^3, 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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Lawrence Ein, Robert Lazarsfeld. 2018-08-13. The Konno invariant of some algebraic varieties. https://arxiv.org/abs/1808.04331

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