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

Date

1997-12-01

Author

Finashin, Sergey
Shustin, Eugenii

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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.

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https://scholar.google.com/citations?view_op=view_citation&hl=en&user=q8Bq2XMAAAAJ&citation_for_view=q8Bq2XMAAAAJ:YOwf2qJgpHMC
https://hdl.handle.net/11511/115321

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Department of Mathematics, Article