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A note on Torelli‐type theorems for Gorenstein curves
Author(s) -
Rizzi Luca,
Zucconi Francesco
Publication year - 2017
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.201600106
Subject(s) - mathematics , infinitesimal , counterexample , pure mathematics , type (biology) , mathematical analysis , discrete mathematics , ecology , biology
Using the notion of generalized divisors introduced by Hartshorne (see [16][R. Hartshorne, 1986]), we adapt the theory of adjoint forms to the case of Gorenstein curves. We show an infinitesimal Torelli‐type theorem for line bundles on Gorenstein curves. We also construct explicit counterexamples to the infinitesimal Torelli claim in the case of a reduced reducible Gorenstein curve.