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

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

1996-07-18

arxiv.org/abs/alg-geom/9607017v1

Mathematics

Algebraic Geometry

AMS-TeX, 9 pages

Scientific paper

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 $d^2$ 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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