Geometry on nodal curves
代数几何
2007-05-23 v1
摘要
Given a family of nodal curves, we construct canonically and compatibly with base-change, via an explicit blow-up of the Cartesian product , a family parametrizing length- subschemes of fibres of (plus some additional data). Though is singular, the important sheaves on it are locally free, which allows us to study intersection theory on it and deduce enumerative applications, including some relative multiple point formulae, enumerating the length- schemes contained simultaneously in some fibre of and some fibre of a given map from to a smooth variety.
引用
@article{arxiv.math/0210209,
title = {Geometry on nodal curves},
author = {Ziv Ran},
journal= {arXiv preprint arXiv:math/0210209},
year = {2007}
}