Positivity of Intersection Multiplicity Over a Two-Dimensional Base
Commutative Algebra
2018-08-02 v2 Algebraic Geometry
Abstract
We show that Serre's Intersection Multiplicity Conjecture holds for a formal power series ring A over a complete, two-dimensional regular local ring R. From this, we deduce the corresponding result for the local rings of any scheme X which is a smooth extension of a regular, two-dimensional base Y. We also investigate the connection between intersection multiplicity and transversality in the unramified setting via a local analysis on the blowup.
Cite
@article{arxiv.1510.05146,
title = {Positivity of Intersection Multiplicity Over a Two-Dimensional Base},
author = {Chris Skalit},
journal= {arXiv preprint arXiv:1510.05146},
year = {2018}
}
Comments
To appear in the Journal of Pure and Applied Algebra. Typos from the original draft have been fixed along with some minor changes in exposition to improve clarity