The jet transcendence degree of a real hypersurface and Huang-Ji-Yau Conjecture

Jan Gregorovic; Ilya Kossovskiy

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arXiv · 2401.01555

The jet transcendence degree of a real hypersurface and Huang-Ji-Yau Conjecture

Jan Gregorovic·Ilya Kossovskiy

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Abstract

We investigate the problem of holomorphic algebraizibility for real hypersurfaces in complex space. We introduce a new invariant of a (real-analytic) Levi-nondegenerate hypersurface called {\em the jet transcendence degree}. Using this invariant, we solve in the negative the Conjecture of Huang, Ji and Yau on the algabraizability of real hypersurfaces with algebraic syzygies.

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Jan Gregorovic, Ilya Kossovskiy. 2024-01-03. The jet transcendence degree of a real hypersurface and Huang-Ji-Yau Conjecture. https://arxiv.org/abs/2401.01555

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