On the Inverse of Monoidal Transformation

Vanishing Theorems on Complete Kähler Manifolds

“…We shall here try to continue the study on the vanishment of the sheaf cohomology groups H ? (X 3 0(E)) which has been performed by Kodaira [10], [11], GrauertRiemenschneider [5], Andreotti-Vesentini [1], [2], Nakano [14], [15], Kazama [9], and others. The purpose of the present paper is to study the cohomology groups on complete Kahler manifolds.…”

“…The purpose of the present paper is to study the cohomology groups on complete Kahler manifolds. Although the spirit is the same as in [1] and [14], we restrict ourselves to C L 2 -cohomology groups' and aim at finding a proper subspace of L 2 -forms for which 8-equation is solvable. We shall prove the following theorem.…”

Asymptotically cylindrical Calabi–Yau 3–folds from weak Fano 3–folds

“…There are two natural projections π ± i : E i → P 1 , (rulings of P 1 × P 1 ) corresponding to a choice of P 1 factor. For each exceptional divisor we make a choice of one of these two rulings; by Nakano [73,28] the fibres of every π ± i can be blown down to yield a non-singular Moishezon 3-fold X , that is, a compact complex 3-fold with three algebraically independent meromorphic functions. Thus we obtain 2 k Moishezon small resolutions X of the nodal 3-fold X in which each singular point P i has been replaced by a non-singular rational curve C i with normal bundle O(−1) ⊕ O(−1).…”

Some remarks on complex Lie groups

“…is Ker ρ-invariant and then induces a Kähler metric on G ∼ = Z × S/ Ker ρ, where s := dim C S and (w 1 , ..., w s ) is a local coordinate system of S. From the technique of Nakano (Proposition 1, [9]), we can find a strictly convex increasing C ∞ function…”