Work

Real plane sextics without real points

Year: 2025

Type: article

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 K 3 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).

Source: Journal of Algebraic Geometry

DOI: 10.1090/jag/844

Authors: Alex Degtyarev, Ilia Itenberg

Institutions: Bilkent University, Centre National de la Recherche Scientifique, Université Paris Cité, Institut de Mathématiques de Jussieu-Paris Rive Gauche, Sorbonne Université

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Agence Nationale de la Recherche

Awards: Tropical aspects of singularities, Symplectic, real, and tropical aspects of enumerative geometry