Open AccessThe rank of the second Gaussian map for general curves
Author(s) -
Alberto Calabri,
Ciro Ciliberto,
Rick Miranda
Publication year - 2011
Publication title -
the michigan mathematical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.763
H-Index - 41
eISSN - 1945-2365
pISSN - 0026-2285
DOI - 10.1307/mmj/1320763048
Subject(s) - mathematics , morphism , invariant (physics) , diagonal , line bundle , combinatorics , pure mathematics , geometry , mathematical physics
We prove that, for the general curve of genus g, the 2nd Gaussian map is injective if g <= 17 and surjective if g >= 18. The proof relies on the study of the limit of the 2nd Gaussian map when the general curve of genus g degenerates to a general stable binary curve, i.e. the union of two rational curves meeting at g+1 points