2007/02/24 by Quang Minh Nguyen, QUANG MINH NGUYEN · 3 citations
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #Polynomial and algebraic computation #math.AG #msc:14C34 #msc:14E20 #msc:14E30 #msc:14H60 #msc:14J70
paper · pdf · doi:10.1142/s0129167x07004230
published as Internat. J. Math., Vol. 18 (2007), No. 5, 535--558 · 21 pages. Supersedes math.AG/0408318. To appear in Internat. J. Math
arxiv created 2007/02/24 · openalex publication_date 2007/05/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Let C be a curve of genus two. We denote by [Formula: see text] the moduli space of semi-stable vector bundles of rank 3 and trivial determinant over C, and by J d the variety of line bundles of degree d on C. In particular, J 1 has a canonical theta divisor Θ. The space [Formula: see text] is a double cover of ℙ 8 = |3Θ| branched along a sextic hypersurface, the Coble sextic. In the dual [Formula: see text], where J 1 is embedded, there is a unique cubic hypersurface singular along J 1 , the Coble cubic. We prove that these two hypersurfaces are dual, inducing a non-abelian Torelli result. Moreover, by looking at some special linear sections of these hypersurfaces, we can observe and reinterpret some classical results of algebraic geometry in a context of vector bundles: the duality of the Segre–Igusa quartic with the Segre cubic, the symmetric configuration of 15 lines and 15 points, the Weddle quartic surface and the Kummer surface.