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arXiv:2106.11392 [math.AG]AbstractReferencesReviewsResources

Noncommutative geometry of elliptic surfaces

Igor Nikolaev

Published 2021-06-21Version 1

We recast elliptic surfaces over the projective line in terms of the non-commutative tori with real multiplication. 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 complex multiplication.

Comments: 11 pages, 2 figures
Categories: math.AG, math.NT, math.OA
Subjects: 11G05, 46L85
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