References & Citations
Mathematics > Algebraic Geometry
Title: Sign involutions on para-abelian varieties
(Submitted on 9 Jan 2023 (v1), last revised 26 Apr 2024 (this version, v2))
Abstract: We study the so-called sign involutions on twisted forms of abelian varieties, and show that such a sign involution exists if and only if the class in the Weil--Ch\^{a}telet group is annihilated by two. If these equivalent conditions hold, we prove that the Picard scheme of the quotient is \'etale and contains no points of finite order. In dimension one, such quotients are Brauer--Severi curves, and we analyze the ensuing embeddings of the genus-one curve into twisted forms of Hirzebruch surfaces and weighted projective spaces.
Submission history
From: Stefan Schröer [view email][v1] Mon, 9 Jan 2023 13:09:45 GMT (20kb,D)
[v2] Fri, 26 Apr 2024 14:03:40 GMT (22kb,D)
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