A Rokhlin Conjecture and Smooth Quotients by the Complex Conjugation of Singular Real Algebraic Surfaces

1999/03/18 by Sergey Finashin, Finashin, Sergey
Mathematics · #14P25 #32S45 #57N13 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:14P25 #msc:32S45 #msc:57N13

paper · pdf · doi:10.48550/arxiv.math/9903112

AMS-TeX,11 pages,2 figures

arxiv created 1999/03/18 · arxiv updated 2009/11/30

Abstract

The topology of the orbit space, Y, for the action of the complex conjugation on a complex surface, X, defined over reals, is studied. I give a criterion for blow-up stable triviality of Y (which implies vanishing of its Seiberg-Witten invariants). The main result concerns the double planes branched along the complexification of reducible real curves with 2 non-singular components. In connection with it, I analize the real singularities of X which become smooth in Y (after taking quotient).

Related

• Rokhlin Conjecture and Topology of Quotients of Complex Surfaces by Complex Conjugation
• The complex separation and extensions of Rokhlin congruence for curves on surfaces
• On imaginary plane curves and Spin quotients of complex surfaces by complex conjugation
• Extensions of Rokhlin congruence for curves on surfaces
• Quotients by complex conjugation for real complete intersection surfaces