Counterexample of Kodaira’s vanishing and Yau’s inequality in higher dimensional variety of characteristic
نویسنده
چکیده
(b) the canonical class K of X is ample and the intersection number (ci.Kn−i) is negative for every i ≥ 2, where ci is the i-th Chern class of X. and (c) there is a finite cover G of X isomorphic to a (P1)n−1-bundle over a nonsingular curve C. The Euler characteristic e(X) of X is equal to e(G) = 2n−1e(C). Put X ′ = X × P and L′ = p1L⊗ p2O(m + 1). Then we have, by Künneth formula, H(X ′, L′−1) ⊇ H1(X,L−1)⊗Hm(Pm,O(−m− 1)) 6= 0.
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