Invariants of algebraic varieties over imperfect fields

2019/03/25 by Tanaka, Hiromu · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1903.10113

Abstract

We introduce four invariants of algebraic varieties over imperfect fields, each of which measures either geometric non-normality or geometric non-reducedness. The first objective of this article is to establish fundamental properties of these invariants. We then apply our results to curves over imperfect fields. In particular, we establish a genus change formula and prove the boundedness of non-smooth regular curves of genus one. We also compute our invariants for some explicit examples.

Cited by

• Varieties with nef anticanonical divisors and Albanese morphisms of relative dimension one in positive characteristic

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