Tohoku Mathematical Journal
2002
September
SECOND SERIES VOL. 54, NO. 3

Tohoku Math. J.
54 (2002), 451-470

Title VANISHING THEOREMS ON TORIC VARIETIES

Author Mircea Mustaţă

(Received August 3, 2000, revised April 25, 2001)
Abstract. We use Cox's description for sheaves on toric varieties and results about local cohomology with respect to monomial ideals to give a characteristic-free approach to vanishing results on toric varieties. As an application, we give a proof of a strong version of Fujita's Conjecture in the case of toric varieties. We also prove that every sheaf on a toric variety corresponds to a module over the homogeneous coordinate ring, generalizing Cox's result for the simplicial case.

2000 Mathematics Subject Classification. Primary 14M25; Secondary 14F17.
Key words and phrases. Toric varieties, homogeneous coordinate ring, vanishing theorems, Fujita's Conjecture.

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