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Title of Journal: Math Ann

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Abbravation: Mathematische Annalen

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Springer Berlin Heidelberg

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DOI

10.1002/adhm.201500003

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ISSN

1432-1807

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Rational curves Dynkin diagrams and Fano manifold

Authors: Roberto Muñoz Gianluca Occhetta Luis E Solá Conde Kiwamu Watanabe
Publish Date: 2014/08/13
Volume: 361, Issue: 3-4, Pages: 583-609
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Abstract

A Fano manifold X with nef tangent bundle is of FlagType if it has the same kind of elementary contractions as a complete flag manifold In this paper we present a method to associate a Dynkin diagram mathcal DX with any such X based on the numerical properties of its contractions We then show that mathcal DX is the Dynkin diagram of a semisimple Lie group As an application we prove that Campana–Peternell conjecture holds when X is a FlagType manifold whose Dynkin diagram is A n ie we show that X is the variety of complete flags of linear subspaces in mathbb PnR Muñoz and L E Solá Conde were partially supported by the Spanish government project MTM200906964 L E Solá Conde was supported by National Researcher Program 20100020413 of NRF L E Solá Conde and K Watanabe were partially supported by the Research in Pairs Program of CIRM K Watanabe was partially supported by JSPS KAKENHI Grant Number 26800002This project was conceived when the third and fourth author enjoyed a grant of the “Research in pairs” program of the Fondazione Bruno Kessler at the Centro Internazionale per la Ricerca Matematica Trento We would like to express our gratitude to this institution for its support and hospitality We would also like to thank J Wiśniewski for his interest in our project and his useful comments

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  1. Estimates of the Green function for X-elliptic operators
  2. Fibred multilinks and singularities $${f \overline g}$$
  3. The NSLUC property and Klee envelope
  4. Hölder estimates for parabolic p ( x , t )-Laplacian systems
  5. Ricci flow on surfaces with cusps
  6. A non-laminar dynamical Green current
  7. Artin characters, Hurwitz trees and the lifting problem
  8. Generic non-selfadjoint Zakharov–Shabat operators
  9. Strichartz estimates via the Schrödinger maximal operator
  10. Examples of relative deformation spaces that are not locally connected
  11. Polynomial approximation of Berkovich spaces and definable types
  12. Prographes sylvestres et groupes profinis presque libres
  13. Zone diagrams in Euclidean spaces and in other normed spaces
  14. A critical radius for unit Hopf vector fields on spheres
  15. Many triangulated 3-spheres
  16. New examples of c 0 -saturated Banach spaces
  17. Relatively weakly open sets in closed balls of Banach spaces, and real JB * -triples of finite rank
  18. The Bergman metric on complete Kähler manifolds
  19. Conformal dimension via subcomplexes for small cancellation and random groups
  20. Analytic torsion of Hirzebruch surfaces
  21. Déformations des cônes de vecteurs primitifs
  22. Radial entire solutions for supercritical biharmonic equations
  23. Weighted Calderón–Zygmund and Rellich inequalities in $$L^p$$
  24. On entropy, regularity and rigidity for convex representations of hyperbolic manifolds
  25. Rigidity of proper holomorphic maps between bounded symmetric domains
  26. On CR Paneitz operators and CR pluriharmonic functions
  27. Absence of wandering domains for some real entire functions with bounded singular sets
  28. Isomonodromic deformations of logarithmic connections and stability
  29. Pointwise equidistribution with an error rate and with respect to unbounded functions
  30. On the Frobenius stable part of Witt vector cohomology
  31. Quantitative mixing results and inner functions
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  37. On Oliver’s p -group conjecture: II
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