Tohoku Mathematical Journal
2009
September
SECOND SERIES VOL. 61, NO. 3

Tohoku Math. J.
61 (2009), 365-392

Title VANISHING THEOREMS FOR DOLBEAULT COHOMOLOGY OF LOG HOMOGENEOUS VARIETIES

Author Michel Brion

(Received December 25, 2008, revised April 2, 2009)
Abstract. 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.

2000 Mathematics Subject Classification. Primary 14M17; Secondary 14F17, 14L30.

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