On uniform flag bundles on Fano manifolds

As a natural extension of the theory of uniform vector bundles on Fano manifolds, we consider uniform principal bundles, and study them by means of the associated flag bundles, as their natural projective geometric realizations. In this paper we develop the necessary background, and prove some theorems that are flag bundle counterparts of some of the central results in the theory of uniform vector bundles.

[1]  Fredrik Meyer,et al.  Representation theory , 2015 .

[2]  G. Elencwajg.  Des fibrés uniformes non homogènes , 1979 .

[3]  R. Muñoz,et al.  Uniform vector bundles on Fano manifolds and applications , 2009, 0911.2606.

[4]  Luis E. Sol'a Conde,et al.  On rank $2$ vector bundles on Fano manifolds , 2011, 1104.1490.

[5]  M. Guyot.  Caractérisation par l'uniformité des fibrés universels sur la Grassmanienne , 1985 .

[6]  W. Ledermann.  INTRODUCTION TO LIE ALGEBRAS AND REPRESENTATION THEORY , 1974 .

[7]  J. Wiśniewski,et al.  On manifolds whose tangent bundle contains an ample subbundle , 2001 .

[8]  E. Sato.  Uniform vector bundles on a projective space , 1976 .

[9]  Luis E. Sol'a Conde,et al.  Fano manifolds whose elementary contractions are smooth $\mathbb P^1$-fibrations , 2014, 1407.3658.

[10]  Johan P. Hansen,et al.  INTERSECTION THEORY , 2011 .

[11]  Xuanyu Pan.  Triviality and Split of Vector Bundles on Rationally Connected Varieties , 2013, 1310.5774.

[12]  C Okonek,et al.  Vector bundles on complex projective space (Corrected reprint of the 1988 Edition) , 2011 .

[13]  Vektorbündel vom rang 2 über dem n-dimensionalen komplex-projektiven raum , 1975 .

[14]  János Kollár,et al.  Rational curves on algebraic varieties , 1995, Ergebnisse der Mathematik und ihrer Grenzgebiete.

[15]  E. Ballico.  Uniform vector bundles on quadrics , 1981, ANNALI DELL UNIVERSITA DI FERRARA.

[16]  Laurent Manivel,et al.  On the projective geometry of rational homogeneous varieties , 2003 .

[17]  O. Debarre.  Higher-Dimensional Algebraic Geometry , 2001 .

[18]  A. Grothendieck.  Sur La Classification Des Fibres Holomorphes Sur La Sphere de Riemann , 1957 .

[19]  P. Ellia.  Sur les fibrés uniformes de rang (n+1) sur [Pn] , 1982 .

[20]  R. Schwarzenberger.  Vector Bundles on the Projective Plane , 1961 .

[21]  C. Casagrande.  Quasi-elementary contractions of Fano manifolds , 2007, Compositio Mathematica.

[22]  R. Muñoz,et al.  Rational curves, Dynkin diagrams and Fano manifolds with nef tangent bundle , 2013, 1304.3928.

[23]  A. V. Ven.  On uniform vector bundles , 1971 .

[24]  Luis E. Sol'a Conde,et al.  Flag bundles on Fano manifolds , 2016, 1601.07299.

[25]  Jarosław A. Wiśniewski,et al.  Uniform Vector Bundles on Fano Manifolds and an Algebraic Proof of Hwang-Mok Characterization of Grassmannians , 2002 .