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Mathematics > Algebraic Geometry
Title: Noncommutative geometry of elliptic surfaces
(Submitted on 21 Jun 2021 (v1), last revised 26 Apr 2024 (this version, v2))
Abstract: We recast elliptic surfaces over the projective line in terms of the non-commutative tori and one-parameter families of the periodic continued fractions. The correspondence is used to study the Picard numbers, the ranks and the minimal models of such surfaces. As an example, we calculate the Picard numbers of elliptic surfaces with fibers having complex multiplication.
Submission history
From: Igor V. Nikolaev [view email][v1] Mon, 21 Jun 2021 20:03:53 GMT (11kb)
[v2] Fri, 26 Apr 2024 17:34:06 GMT (12kb)
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