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Online ISSN 1534-7486; Print ISSN 1056-3911
Real plane sextics without real points
Authors:
Alex Degtyarev and Ilia Itenberg
Journal:
J. Algebraic Geom. 34 (2025), 543-577
DOI:
https://doi.org/10.1090/jag/844
Published electronically:
March 24, 2025
Full-text PDF
Abstract | References | Additional Information
Abstract: We prove that the equisingular deformation type of a simple real plane sextic curve with smooth real part is determined by its real homological type, i.e., the polarization, exceptional divisors, and real structure recorded in the homology of the covering $K3$-surface. As an illustration, we obtain an equisingular deformation classification of real plane sextics with empty real part (for completeness, we consider the few non-simple ones as well).
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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
Ilia Itenberg
Affiliation:
IMJ-PRG, Sorbonne Université and Université Paris Cité, CNRS, F-75005 Paris, France
MR Author ID:
321564
ORCID:
0000-0003-3216-1581
Email:
ilia.itenberg@imj-prg.fr
Received by editor(s):
March 12, 2024
Received by editor(s) in revised form:
September 15, 2024, and October 18, 2024
Published electronically:
March 24, 2025
Additional Notes:
The first author was partially supported by the TÜBİTAK grant 123F111. The second author was supported in part by the ANR grants ANR-18-CE40-0009 ENUMGEOM and ANR-22-CE40-0014 SINTROP.
Article copyright:
© Copyright 2025
University Press, Inc.