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arXiv · 1903.10113

Invariants of algebraic varieties over imperfect fields

Hiromu Tanaka
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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.

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Hiromu Tanaka. 2020-10-13. Invariants of algebraic varieties over imperfect fields. https://arxiv.org/abs/1903.10113

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