Tropicalization of theta characteristics, double covers, and Prym varieties

Let Ci, i=1,2, be two smooth non-hyperelliptic curves over the complex numbers of genus g≥ 3, and [Formula: see text] connected étale double covers, such that the theta divisors Ξi of the associated Prym varieties (pi, Ξi) are non singular in codimension ≤ 3. If [Formula: see text] are the norm maps, then Ξi is isomorphic to {[Formula: see text] and h0 (L) is even and positive}. Then the Abel maps define generic ℙ1 bundles Xi→Ξi, where Xi is the special divisor variety [Formula: see text] and [Formula: see text] even}. We prove, under the hypotheses above, that biregular isomorphism of the special divisor varieties X1≅ X2 implies isomorphism of the double covers [Formula: see text].

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SPIN VERLINDE SPACES AND PRYM THETA FUNCTIONS

Proceedings of the London Mathematical Society ◽

10.1112/s0024611599001665 ◽

1999 ◽

Vol 78 (1) ◽

pp. 52-76 ◽

Cited By ~ 2

Author(s):

W. M. OXBURY

Keyword(s):

Line Bundle ◽

Moduli Space ◽

Algebraic Curve ◽

Theta Functions ◽

Prym Varieties ◽

Theta Characteristics

It is shown that the theta functions of level $n$ on the principally polarised Prym varieties of an algebraic curve are dual to the sections of the orthogonal theta line bundle on the moduli space of Spin($n$)-bundles over the curve. As a by-product of our computations, we also note that when $n$ is odd, the Pfaffian line bundle on moduli space has a basis of sections labelled by the even theta characteristics of the curve.

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A DUALITY FOR SPIN VERLINDE SPACES AND PRYM THETA FUNCTIONS

Journal of the London Mathematical Society ◽

10.1017/s0024610701002095 ◽

2001 ◽

Vol 63 (3) ◽

pp. 513-532 ◽

Cited By ~ 2

Author(s):

C. PAULY ◽

S. RAMANAN

Keyword(s):

Line Bundle ◽

Moduli Space ◽

Theta Functions ◽

Projective Curve ◽

Smooth Projective Curve ◽

Prym Varieties ◽

Dual Spaces ◽

Double Covers ◽

Determinant Line Bundle

The paper proves canonical isomorphisms between Spin Verlinde spaces, that is, spaces of global sections of a determinant line bundle over the moduli space of semistable Spinn-bundles over a smooth projective curve C, and the dual spaces of theta functions over Prym varieties of unramified double covers of C.

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Generalization of the Symmetric Starter of the Orthogonal Double Covers of the Complete Bipartite Graph

Menoufia Journal of Electronic Engineering Research ◽

10.21608/mjeer.2006.64856 ◽

2006 ◽

Vol 16 (2) ◽

pp. 171-177

Author(s):

S. A. El-Serafi ◽

R. A. El-Shanawany ◽

M. Sh. Higazy

Keyword(s):

Bipartite Graph ◽

Complete Bipartite Graph ◽

Double Covers

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Double cover K3 surfaces of Hirzebruch surfaces

Advances in Geometry ◽

10.1515/advgeom-2020-0034 ◽

2021 ◽

Vol 21 (2) ◽

pp. 221-225

Author(s):

Taro Hayashi

Keyword(s):

Rational Surface ◽

K3 Surfaces ◽

Double Cover ◽

Double Covering ◽

Smooth Surfaces ◽

Branch Locus ◽

Hirzebruch Surfaces ◽

Double Covers

Abstract General K3 surfaces obtained as double covers of the n-th Hirzebruch surfaces with n = 0, 1, 4 are not double covers of other smooth surfaces. We give a criterion for such a K3 surface to be a double covering of another smooth rational surface based on the branch locus of double covers and fibre spaces of Hirzebruch surfaces.

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