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Vanishing thetanull and hyperelliptic curves
Author(s) -
Schneider Olivier
Publication year - 2007
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200310492
Subject(s) - mathematics , moduli space , locus (genetics) , hyperelliptic curve , hyperelliptic curve cryptography , genus , intersection (aeronautics) , pure mathematics , component (thermodynamics) , combinatorics , botany , geography , computer science , physics , public key cryptography , cartography , thermodynamics , elliptic curve cryptography , biology , gene , operating system , encryption , biochemistry , chemistry
Let ℳ g ,2 be the moduli space of curves of genus g with a level‐2 structure. We prove here that there is always a non hyperelliptic element in the intersection of four thetanull divisors in ℳ 6,2 . We prove also that for all g ≥ 3, each component of the hyperelliptic locus in ℳ g ,2 is a connected component of the intersection of g – 2 thetanull divisors. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)