Vanishing theorems for Dolbeault cohomology of log homogeneous varieties
Brion, Michel
Tohoku Math. J. (2), Tome 61 (2009) no. 1, p. 365-392 / Harvested from Project Euclid
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We consider a complete nonsingular complex algebraic variety having a normal crossing divisor such that the associated logarithmic tangent bundle is generated by its global sections. We obtain an optimal vanishing theorem for logarithmic Dolbeault cohomology of nef line bundles in that setting. This implies a vanishing theorem for ordinary Dolbeault cohomology which generalizes results of Broer for flag varieties, and of Mavlyutov for toric varieties.
Publié le : 2009-05-15
Classification:  14M17,  14F17,  14L30 
@article{1255700200,
     author = {Brion, Michel},
     title = {Vanishing theorems for Dolbeault cohomology of log homogeneous varieties},
     journal = {Tohoku Math. J. (2)},
     volume = {61},
     number = {1},
     year = {2009},
     pages = { 365-392},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1255700200}
}

Brion, Michel. Vanishing theorems for Dolbeault cohomology of log homogeneous varieties. Tohoku Math. J. (2), Tome 61 (2009) no. 1, pp.  365-392. http://gdmltest.u-ga.fr/item/1255700200/