Geodesic
Bounds for the anticanonical bundle of a homogeneous projective rational manifold
Documenta mathematica, Tome 9 (2004), pp. 251-263
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The following bounds for the anticanonical bundle KX∗​=detTX​ of a complex homogeneous projective rational manifold X of dimension n are established: newcommandbinom[2]#1choose#2 3n≤dimH0(X,KX∗​)≤(n2n+1​)and2nn!≤degKX∗​≤(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.
DOI : 10.4171/dm/166
Classification : 14M15, 14M17, 32M10 
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     author = {Dennis Snow},
     title = {Bounds for the anticanonical bundle of a homogeneous projective rational manifold},
     journal = {Documenta mathematica},
     pages = {251--263},
     year = {2004},
     volume = {9},
     doi = {10.4171/dm/166},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/166/}
}
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Dennis Snow. Bounds for the anticanonical bundle of a homogeneous projective rational manifold. Documenta mathematica, Tome 9 (2004), pp. 251-263. doi: 10.4171/dm/166

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