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.
Citation
Hiromu Tanaka. "Invariants of algebraic varieties over imperfect fields." Tohoku Math. J. (2) 73 (4) 471 - 538, 2021. https://doi.org/10.2748/tmj.20200611
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