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Asymptotic period relations for Jacobian elliptic surfaces

Research output: Contribution to journalArticle

Original languageEnglish
Article numberPROC191212
Number of pages42
JournalPROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY
Volume2020
DOIs
Accepted/In press24 May 2020
Published14 Jul 2020

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Abstract

We describe the image of the locus of hyperelliptic curves of genus (Formula presented.) under the period mapping in a neighbourhood of the diagonal locus (Formula presented.). There is just one branch for each of the alkanes (Formula presented.) of elementary organic chemistry, and each branch has a simple linear description in terms of the entries of the period matrix. This picture is replicated for simply connected Jacobian elliptic surfaces, which form the next simplest class of algebraic surfaces after K3 and abelian surfaces. In the period domain for such surfaces of geometric genus (Formula presented.), there is a locus (Formula presented.) that is analogous to (Formula presented.), and the image of the moduli space under the period map has just one branch through (Formula presented.) for each alkane. Each branch is smooth and has an explicit description as a vector bundle of rank (Formula presented.) over a domain that contains (Formula presented.).

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