Symmetric theta divisors of Klein surfaces

• Autorzy: Christian Okonek , Andrei Teleman
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

Kategorie tematyczne

• 14H60: Vector bundles on curves and their moduli
• 14H55: Riemann surfaces; Weierstrass points; gap sequences
• 14H40: Jacobians, Prym varieties

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2012
• Tom: 10
• Numer: 4
• Strony: 1314-1320

Daty

wydano

2012-08-01

online

2012-05-31

Twórcy

autor

Christian Okonek

• Universität Zürich

autor

Andrei Teleman

• Université de Provence

Bibliografia

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• [8] Libgober A., Theta characteristics on singular curves, spin structures and Rohlin theorem, Ann. Sci. École Norm. Sup., 1988, 21(4), 623–635
• [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
• [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
• [11] Schaffhauser F., Moduli spaces of vector bundles over a Klein surface, Geom. Dedicata, 2011, 151, 187–206 http://dx.doi.org/10.1007/s10711-010-9526-3
• [12] Wang S., A Narasimhan-Seshadri-Donaldson correspondence over non-orientable surfaces, Forum Math., 1996, 8(4), 461–474 http://dx.doi.org/10.1515/form.1996.8.461

Identyfikatory

DOI

10.2478/s11533-012-0048-0