ON IMAGINARY PLANE CURVES AND SPIN QUOTIENTS OF COMPLEX SURFACES BY COMPLEX CONJUGATION


Finashin S., Shustin E.

Amer Math Soc Transl (2), vol.180, pp.93-102, 1997 (Peer-Reviewed Journal)

  • Publication Type: Article / Article
  • Volume: 180
  • Publication Date: 1997
  • Journal Name: Amer Math Soc Transl (2)
  • Page Numbers: pp.93-102
  • Middle East Technical University Affiliated: Yes

Abstract

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.