Research Information System
Amer Math Soc Transl (2), vol.180, pp.93-102, 1997 (Peer-Reviewed Journal)
It is proved that for any topological or analytical types of isolated singular points of plane curves, there exists a nonreal irreducible plane algebraic curve of degree d that passes through d² real distinct points and has imaginary singular points of given types. This result is used to construct a series of examples of complex algebraic surfaces X defined over R whose quo-tients Y= X/conj by the complex conjugation conj are Spin simply connected 4-manifolds with signature 16k, for an arbitrary integer k> 0. In the previously known examples the signature of Spin simply connected quotients Y was zero.