Geodesic
Bounds for the anticanonical bundle of a homogeneous projective rational manifold
Documenta mathematica, Tome 9 (2004), pp. 251-263.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: The following bounds for the anticanonical bundle $K_X^{*} = \det T_X$ of a complex homogeneous projective rational manifold $X$ of dimension $n$ are established: newcommandbinom[2]#1choose#2 $$ 3^n \le \dim H^0(X,K_X^{*}) \le \binom{2n+1}n\quad\mathrm{and}\quad 2^n n! \le \deg K_X^{*} \le (n+1)^n $$ with equality in the lower bounds if and only if $X$ is a flag manifold and equality in the upper bounds if and only if $X$ is complex projective space. None of these bounds holds for general Fano manifolds.
Classification : 14M17, 14M15, 32M10 
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     author = {Snow, Dennis},
     title = {Bounds for the anticanonical bundle of a homogeneous projective rational manifold},
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Snow, Dennis. Bounds for the anticanonical bundle of a homogeneous projective rational manifold. Documenta mathematica, Tome 9 (2004), pp. 251-263. http://geodesic.mathdoc.fr/item/DOCMA_2004__9__a16/