On imaginary plane curves and Spin quotients of complex surfaces by complex conjugation

1996/07/18 by Sergey Finashin, Eugenii Shustin, Finashin, Sergey +1
Mathematics · #14P25 #57N13 #Algebraic Geometry (math.AG) #FOS: Mathematics #alg-geom #math.AG #msc:14P25 #msc:57N13

paper · pdf · doi:10.48550/arxiv.alg-geom/9607017

AMS-TeX, 9 pages

arxiv created 1996/07/18 · arxiv updated 2009/11/30

Abstract

It is proven that for any topological or analytical types of isolated singular points of plane curves, there exists a non-real irreducible plane algebraic curve of degree d which goes through d² real distinct points and has imaginary singular points of the given types. This result is used to construct a series of examples of complex algebraic surfaces X defined over \R whose quotients Y=X/\conj by the complex conjugation \conj are Spin simply connected 4-manifolds with signature 16k, for arbitrary integer k>0.

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