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Uniform Vector Bundles on Fano Manifolds and an Algebraic Proof of Hwang-Mok Characterization of Grassmannians

In: Complex Geometry

Author

Listed:
  • Jarosław A. Wiśniewski

    (Warsaw University, Institute of Mathematics)

Abstract

A projective manifold X is called Fano if its anticanonical divisor − K x is ample. Fano manifolds form a very distinguished class: in each dimension there is only a finite number of deformation classes of them and they are classified in dimension ≤ 3, the case dim X = 3 due to Fano, Roth, Iskovskih and Shokurov. In dimension ≥ 4 not much is known about Fano manifolds in general. However, due to results of Mori, Kawamata and Shokurov, Fano manifolds with Picard number ρ(X) bigger than 1 admit special morphisms, called Fano-Mori contractions, which can be used to study the structure of such Fano’s. The case ρ(X) = 1 seems to be harder to approach, see [IP] for an overview on Fano varieties.

Suggested Citation

  • Jarosław A. Wiśniewski, 2002. "Uniform Vector Bundles on Fano Manifolds and an Algebraic Proof of Hwang-Mok Characterization of Grassmannians," Springer Books, in: Ingrid Bauer & Fabrizio Catanese & Thomas Peternell & Yujiro Kawamata & Yum-Tong Siu (ed.), Complex Geometry, pages 329-340, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-56202-0_17
    DOI: 10.1007/978-3-642-56202-0_17
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