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arXiv · 2601.10055

Kov\'acs' conjecture on characterization of projective space and hyperquadrics

Soham Ghosh
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Abstract

We prove Kov\'acs' conjecture that claims that if the $p^{th}$ exterior power of the tangent bundle of a smooth complex projective variety contains the $p^{th}$ exterior power of an ample vector bundle then the variety is either projective space or the $p$-dimensional quadric hypersurface. We also prove a similar characterization involving symmetric powers instead of exterior powers. This provides a common generalization of Mori, Wahl, Cho-Sato, Andreatta-Wi\'sniewski, Kobayashi-Ochiai, and Araujo-Druel-Kov\'acs type characterizations of such varieties.

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Soham Ghosh. 2026-01-15. Kov\'acs' conjecture on characterization of projective space and hyperquadrics. https://arxiv.org/abs/2601.10055

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