Tohoku Mathematical Journal

Vanishing theorems for Dolbeault cohomology of log homogeneous varieties

Michel Brion

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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.

Article information

Tohoku Math. J. (2), Volume 61, Number 3 (2009), 365-392.

First available in Project Euclid: 16 October 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14M17: Homogeneous spaces and generalizations [See also 32M10, 53C30, 57T15]
Secondary: 14F17: Vanishing theorems [See also 32L20] 14L30: Group actions on varieties or schemes (quotients) [See also 13A50, 14L24, 14M17]


Brion, Michel. Vanishing theorems for Dolbeault cohomology of log homogeneous varieties. Tohoku Math. J. (2) 61 (2009), no. 3, 365--392. doi:10.2748/tmj/1255700200.

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