# Symmetric theta divisors of Klein surfaces

Christian Okonek; Andrei Teleman

Open Mathematics (2012)

- Volume: 10, Issue: 4, page 1314-1320
- ISSN: 2391-5455

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topChristian Okonek, and Andrei Teleman. "Symmetric theta divisors of Klein surfaces." Open Mathematics 10.4 (2012): 1314-1320. <http://eudml.org/doc/269734>.

@article{ChristianOkonek2012,

abstract = {This is a slightly expanded version of the talk given by the first author at the conference Instantons in complex geometry, at the Steklov Institute in Moscow. The purpose of this talk was to explain the algebraic results of our paper Abelian Yang-Mills theory on Real tori and Theta divisors of Klein surfaces. In this paper we compute determinant index bundles of certain families of Real Dirac type operators on Klein surfaces as elements in the corresponding Grothendieck group of Real line bundles in the sense of Atiyah. On a Klein surface these determinant index bundles have a natural holomorphic description as theta line bundles. In particular we compute the first Stiefel-Whitney classes of the corresponding fixed point bundles on the real part of the Picard torus. The computation of these classes is important, because they control to a large extent the orientability of certain moduli spaces in Real gauge theory and Real algebraic geometry.},

author = {Christian Okonek, Andrei Teleman},

journal = {Open Mathematics},

keywords = {Klein surfaces; Symmetric theta divisors; Appell-Humbert data; Yang-Mills connections; Real vector bundles; symmetric theta divisors; real vector bundles},

language = {eng},

number = {4},

pages = {1314-1320},

title = {Symmetric theta divisors of Klein surfaces},

url = {http://eudml.org/doc/269734},

volume = {10},

year = {2012},

}

TY - JOUR

AU - Christian Okonek

AU - Andrei Teleman

TI - Symmetric theta divisors of Klein surfaces

JO - Open Mathematics

PY - 2012

VL - 10

IS - 4

SP - 1314

EP - 1320

AB - This is a slightly expanded version of the talk given by the first author at the conference Instantons in complex geometry, at the Steklov Institute in Moscow. The purpose of this talk was to explain the algebraic results of our paper Abelian Yang-Mills theory on Real tori and Theta divisors of Klein surfaces. In this paper we compute determinant index bundles of certain families of Real Dirac type operators on Klein surfaces as elements in the corresponding Grothendieck group of Real line bundles in the sense of Atiyah. On a Klein surface these determinant index bundles have a natural holomorphic description as theta line bundles. In particular we compute the first Stiefel-Whitney classes of the corresponding fixed point bundles on the real part of the Picard torus. The computation of these classes is important, because they control to a large extent the orientability of certain moduli spaces in Real gauge theory and Real algebraic geometry.

LA - eng

KW - Klein surfaces; Symmetric theta divisors; Appell-Humbert data; Yang-Mills connections; Real vector bundles; symmetric theta divisors; real vector bundles

UR - http://eudml.org/doc/269734

ER -

## References

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- [9] Okonek Ch., Teleman A., Gauge theoretical equivariant Gromov-Witten invariants and the full Seiberg-Witten invariants of ruled surfaces, Comm. Math. Phys., 2002, 227(3), 551–585 http://dx.doi.org/10.1007/s002200200637 Zbl1037.57025
- [10] Okonek Ch., Teleman A., Abelian Yang-Mills theory on Real tori and Theta divisors of Klein surfaces, preprint available at http://arxiv.org/abs/1011.1240
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