Curves and symmetric spaces, II
成果类型：
Article
署名作者：
Mukai, Shigeru
刊物名称：
ANNALS OF MATHEMATICS
ISSN/ISSBN：
0003-486X
DOI：
10.4007/annals.2010.172.1539
发表日期：
2010
页码：
1539-1558
关键词：
摘要：
Let Sym(3) C -> P-*(k circle plus Sym(3) k circle plus Sym(3) k circle plus k) = P-13, A bar right arrow (1 : A : A' : det A) be the Veronese embedding of the space of symmetric matrices of degree 3, where A' is the cofactor matrix of A. The closure SpG(3, 6) of this image is a 6-dimensional homogeneous variety of the symplectic group Sp(3). A canonical curve C-16 subset of P-8 of genus 9 over a perfect field k is isomorphic to a complete linear section of this projective variety SpG(3, 6) subset of P-13 unless C circle times(k) (k) over bar, (k) over bar being the algebraic closure, is a covering of degree at most 5 of the projective line. We prove this by means of linear systems of higher rank.