## 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.).

Original language | English |
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Article number | PROC191212 |

Number of pages | 42 |

Journal | PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY |

Volume | 0 |

Issue number | 0 |

Early online date | 14 Jul 2020 |

DOIs | |

Publication status | E-pub ahead of print - 14 Jul 2020 |

## Keywords

- 14H42 (primary)
- 14J27
- 32G20 (secondary)