English

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}
}