Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

On deformations of singular plane sextics


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
Email: degt@fen.bilkent.edu.tr

DOI: https://doi.org/10.1090/S1056-3911-07-00469-9
Received by editor(s): December 8, 2005
Received by editor(s) in revised form: November 27, 2006
Published electronically: August 6, 2007

American Mathematical Society