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

Sergey Finashin·Eugenii Shustin
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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 $d^2$ 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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BibTeXRIS

Sergey Finashin, Eugenii Shustin. 1996-07-18. On imaginary plane curves and Spin quotients of complex surfaces by complex conjugation. https://arxiv.org/abs/alg-geom/9607017

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