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arXiv · 1510.05146

Positivity of Intersection Multiplicity Over a Two-Dimensional Base

Chris Skalit
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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.

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Chris Skalit. 2018-07-31. Positivity of Intersection Multiplicity Over a Two-Dimensional Base. https://arxiv.org/abs/1510.05146

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