scholarly journals The double ramification cycle and the theta divisor

2014 ◽  
Vol 142 (12) ◽  
pp. 4053-4064 ◽  
Author(s):  
Samuel Grushevsky ◽  
Dmitry Zakharov
Keyword(s):  
Theta Divisor ◽  
Double Ramification Cycle

scholarly journals Pixton’s double ramification cycle relations

2018 ◽  
Vol 22 (2) ◽  
pp. 1069-1108 ◽  
Author(s):  
Emily Clader ◽  
Felix Janda
Keyword(s):  
Double Ramification Cycle

scholarly journals VECTOR BUNDLES, DUALITIES AND CLASSICAL GEOMETRY ON A CURVE OF GENUS TWO

2007 ◽  
Vol 18 (05) ◽  
pp. 535-558 ◽  
Author(s):  
QUANG MINH NGUYEN
Keyword(s):  
Vector Bundles ◽  
Double Cover ◽  
Line Bundles ◽  
Theta Divisor ◽  
Quartic Surface ◽  
Stable Vector Bundles ◽  
Symmetric Configuration ◽  
Classical Geometry ◽  
Genus Two ◽  
Linear Sections

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 Jd the variety of line bundles of degree d on C. In particular, J1 has a canonical theta divisor Θ. The space [Formula: see text] is a double cover of ℙ8 = |3Θ| branched along a sextic hypersurface, the Coble sextic. In the dual [Formula: see text], where J1 is embedded, there is a unique cubic hypersurface singular along J1, 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.

scholarly journals The loci of abelian varieties with points of high multiplicity on the theta divisor

2008 ◽  
Vol 139 (1) ◽  
pp. 233-247 ◽  
Author(s):  
Samuel Grushevsky ◽  
Riccardo Salvati Manni
Keyword(s):  
Abelian Varieties ◽  
High Multiplicity ◽  
Theta Divisor

scholarly journals Powers of the Theta Divisor and Relations in the Tautological Ring

2017 ◽  
Vol 2018 (24) ◽  
pp. 7725-7754 ◽  
Author(s):  
Emily Clader ◽  
Samuel Grushevsky ◽  
Felix Janda ◽  
Dmitry Zakharov
Keyword(s):  
Theta Divisor ◽  
Tautological Ring

The theta divisor of $SU_C(2,2d)^s$ is not hyperelliptic

1996 ◽  
Vol 82 (3) ◽  
pp. 503-552 ◽  
Author(s):  
Sonia Brivio ◽  
Alessandro Verra
Keyword(s):  
Theta Divisor

scholarly journals RANK FOUR SYMPLECTIC BUNDLES WITHOUT THETA DIVISORS OVER A CURVE OF GENUS TWO

2008 ◽  
Vol 19 (04) ◽  
pp. 387-420 ◽  
Author(s):  
GEORGE H. HITCHING
Keyword(s):  
Line Bundle ◽  
Moduli Space ◽  
Vector Bundles ◽  
Projective Variety ◽  
Theta Divisor ◽  
Weierstrass Points ◽  
Base Locus ◽  
Canonical Bijection ◽  
Genus Two ◽  
Irreducible Projective Variety

The moduli space [Formula: see text] of rank four semistable symplectic vector bundles over a curve X of genus two is an irreducible projective variety of dimension ten. Its Picard group is generated by the determinantal line bundle Ξ. The base locus of the linear system |Ξ| consists of precisely those bundles without theta divisors, that is, admitting nonzero maps from every line bundle of degree -1 over X. We show that this base locus consists of six distinct points, which are in canonical bijection with the Weierstrass points of the curve. We relate our construction of these bundles to another of Raynaud and Beauville using Fourier–Mukai transforms. As an application, we prove that the map sending a symplectic vector bundle to its theta divisor is a surjective map from [Formula: see text] to the space of even 4Θ divisors on the Jacobian variety of the curve.

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