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Characterizations of smooth projective horospherical varieties of Picard number one.

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Titel: Characterizations of smooth projective horospherical varieties of Picard number one.
Autoren: Hong, Jaehyun1 (AUTHOR) jhhong00@ibs.re.kr, Kim, Shin-young2,3 (AUTHOR) shinyoungkim@ibs.re.kr
Quelle: Selecta Mathematica, New Series. Feb2025, Vol. 31 Issue 1, p1-46. 46p.
Schlagwörter: *PICARD number, *MATHEMATICAL equivalence, *LIE algebras, *VECTOR bundles, *MATHEMATICS
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. [ABSTRACT FROM AUTHOR]
Datenbank: Academic Search Index
Beschreibung
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. [ABSTRACT FROM AUTHOR]
ISSN:10221824
DOI:10.1007/s00029-024-00997-5