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math.CV2024
Holomorphic vector fields with real integral manifolds
Martin Kolář, Ilya Kossovskiy, Bernhard Lamel
We classify singular holomorphic vector fields in two-dimensional complex space admitting a (Levi-nonflat) real-analytic invariant 3-fold through the singularity. In this way, we c…
math.CV2024
The jet transcendence degree of a real hypersurface and Huang-Ji-Yau Conjecture
Jan Gregorovic, Ilya Kossovskiy
We investigate the problem of holomorphic algebraizibility for real hypersurfaces in complex space. We introduce a new invariant of a (real-analytic) Levi-nondegenerate hypersurfac…