Looking for rational curves on cubic hypersurfaces
Algebraic Geometry
2007-10-31 v1 Number Theory
Abstract
These are the substantially expanded notes of the lectures of JK at the summer school "Higher-Dimensional Geometry over Finite Fields" in G\"ottingen, June 2007. The first part gives an overview of the methods. The main new result is the construction of rational curves passing through a given collection of points on smooth cubic hypersurfaces over finite fields.
Cite
@article{arxiv.0710.5516,
title = {Looking for rational curves on cubic hypersurfaces},
author = {János Kollár and Ulrich Derenthal},
journal= {arXiv preprint arXiv:0710.5516},
year = {2007}
}