On deformations of singular plane sextics

Degtyarev, Alex

doi:10.1090/S1056-3911-07-00469-9

Author: Alex Degtyarev
Journal: J. Algebraic Geom. 17 (2008), 101-135
DOI: https://doi.org/10.1090/S1056-3911-07-00469-9
Published electronically: August 6, 2007
MathSciNet review: 2357681
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Abstract | References | Additional Information

Abstract: We study complex plane projective sextic curves with simple singularities up to equisingular deformations. It is shown that two such curves are deformation equivalent if and only if the corresponding pairs are diffeomorphic. A way to enumerate all deformation classes is outlined, and a few examples are considered, including classical Zariski pairs; in particular, promising candidates for homeomorphic but not diffeomorphic pairs are found.

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Additional Information

Alex Degtyarev
Affiliation: Department of Mathematics, Bilkent University, 06800 Ankara, Turkey
MR Author ID: 271103
ORCID: 0000-0001-6586-4094
Email: degt@fen.bilkent.edu.tr

Received by editor(s): December 8, 2005
Received by editor(s) in revised form: November 27, 2006
Published electronically: August 6, 2007