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arXiv · 2203.10313

Characterizations of smooth projective horospherical varieties of Picard number one

Jaehyun Hong·Shin-young Kim
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Abstract

Let $X$ be a smooth projective horospherical variety of Picard number one. We show that a uniruled projective manifold of Picard number one is biholomorphic to $X$ if its variety of minimal rational tangents at a general point is projectively equivalent to that of $X$. To get a local flatness of the geometric structure arising from the variety of minimal rational tangents, we apply the methods of $W$-normal complete step prolongations. We compute the associated Lie algebra cohomology space of degree two and show the vanishing of holomorphic sections of the vector bundle having this cohomology space as a fiber.

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Jaehyun Hong, Shin-young Kim. 2022-03-19. Characterizations of smooth projective horospherical varieties of Picard number one. https://doi.org/10.1007/s00029-024-00997-5

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