The Konno invariant of some algebraic varieties
Algebraic Geometry
2018-08-14 v1
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.
Keywords
Cite
@article{arxiv.1808.04331,
title = {The Konno invariant of some algebraic varieties},
author = {Lawrence Ein and Robert Lazarsfeld},
journal= {arXiv preprint arXiv:1808.04331},
year = {2018}
}