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Real abelian varieties and real algebraic curves. (English) Zbl 0895.14013

Broglia, Fabrizio (ed.), Lectures in real geometry. Elaborated versions of the lectures given at the winter school in real geometry, Madrid, Spain, January 3–7, 1994. Berlin: de Gruyter. De Gruyter Expo. Math. 23, 167-256 (1996).
This is an expository paper on the theory of real abelian varieties and its applications to curves. First the authors introduce basic notions on complex tori, then they discuss the main concepts regarding real algebraic varieties and real structures on complex varieties. The last part presents applications to real curves. The authors explain the relation of algebraic invariants of a real structure on a compact Riemann surface with topological invariants of the real locus. Many of the ideas presented arised from work of Comesatti.
For the entire collection see [Zbl 0856.00014].

MSC:

14K20 Analytic theory of abelian varieties; abelian integrals and differentials
14H55 Riemann surfaces; Weierstrass points; gap sequences
14P15 Real-analytic and semi-analytic sets
32C05 Real-analytic manifolds, real-analytic spaces
30F10 Compact Riemann surfaces and uniformization
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