arXiv subjects
Publications and source records attributed to Hajime Tsuji.
In this note we shall prove that the complete Kähler-Einstein volume form on a bounded strongly pseudoconvex domain with $C^{\infty}$-boundary is the normalized limit of a sequence of Bergman kernels.
In this article we construct a canonical Kähler-Einstein current on a LC (log canonical) pairs of log general type as the limit of a sequence of canonical Kähler-Einstein currents on KLT(Kawamata log terminal) pairs of log general type. We call the volume form associated with the canonical Kähler-Einstein current the canonical measure of the LC pair. We prove that the relative canonical measure on a projective family of LC pairs of log general type defines a singular hermitian metric on the relative log canonical bundle and the metric has semipositive curvature in the sense of current. This is the first semipositivity result for relative log canonical bundles of a family of LC pairs in general dimension. Our proof depends on certain Ricci iterations and dynamical systems of Bergman kernels.
In this article, we construct the canonical semipositive current or the canonical measure ($=$ the potential of the canonical semipositive current) on a smooth projective variety of nonnegative Kodaira dimension in terms of a dynamical system of Bergman kernels. This current is considered to be a generalization of a Kähler-Einstein metric and coincides the one constructed independently by J. Song and G. Tian. The major difference between their work and the present article is that they found the canonical measure in terms of Käher-Ricci flows, while I found the canonical measure in terms of the dynamical system of Bergman kernels. Hence the present approach can be viewed as the discrete version of the Kähler-Ricci flow.
We prove global generation of the direct images of relative pluricanonical systems of sufficiently large and divisible multiples over the complement of the discriminant locus.
This supersedes 0704.0566. We prove the invariance of logarithmic plurigenera for a projective family of KLT pairs and the adjoint line bundle of KLT line bundles. The proof uses the canonical singular hermitian metrics on relative logcanonical bundles.
We introduce a new class of canonical AZD's (called the supercanonical AZD's) on the canonical bundles of smooth projective varieties with pseudoeffective canonical classes. We study the variation of the supercanonical AZD $\hat{h}_{can}$ under projective deformations and give a new proof of the invariance of plurigenera.
In this paper, I prove a very general extension theorem for log pluricanonical systems. The main application of this extension theorem is (together with Kawamata's subadjunction theorem) to give an optimal subadjunction theorem which relates the positivities of canonical bundle of the ambient projective manifold and that of the (maximal) center of log canonical singularities. This is an extension of the corresponding result in my previous work where I dealt with log pluricanonical systems of general type. This subadjunction theorem indicates an approach to solve the abundance conjecture for canonical divisors (or log canonical divisors) in terms of the induction in dimension.
We construct a canonical singular hermitian metric with semipositive curvature current on the canonical line bundle of a compact Kähler manifold with pseudoeffective canonical bundle.
We prove semipositivity of the curvature of the Narashimhan-Simha metric on an arbitrary flat projective family of varieties with only canonical singularities. This also implies that the direct image of pluricanonical systems have a natural continuous hermitian strucutre with semipositive curvature curvature current in the sense of Nakano. This is an improvement of the author's preprint ``Refined semipositivity and moduli of canonical models (2005)''.
In this paper, I give a new construction of a Kähler-Einstein metrics on a smooth projective variety with ample canonical bundle. This result can be generalized to the construction of a singular Kähler-Einstein metric on a smooth projective variety of general type which gives an AZD of the canonical bundle. Also the variation of Bergman kernels and Kähler-Einstein volume form have been considered.
Generalizing the recent result of Berndtsson, we prove the Nakano semipositivity of the direct image of relative pluricanonical systems and the direct image of relative adjoint (singular) hermitian line bundle with semipositive curvature. This gives a new proof of Kawamata's theorem on the semipositivity of the direct image of relative pluricanonical systems.
This is a revised version of the second half of my paper math.AG/9909021. We prove that there exists a positive integer $ν_{n}$ depending only on $n$ such that for every smooth projective $n$-fold of general type $X$ defined over complex numbers, $\mid mK_{X}\mid$ gives a birational rational map from $X$ into a projective space for every $m\geq ν_{n}$.
We prove that there exists a positive integer $ν_{n}$ depending only on $n$ such that for every smooth projective $n$-fold of general type $X$ defined over {\bf C}, $\mid mK_{X}\mid$ gives a birational rational map from $X$ into a projective space for every $m\geq ν_{n}$. This theorem gives an affirmative answer to Severi's conjecture. The key ingredients of the proof are the theory of AZD which was originated by the aurhor and the subadjunction formula for AZD's of logcanoncial divisors.
We prove that for every positive integer $m\geq 18(2^{9}\cdot 3^{7})!$ and every smooth projective 3-fold of general type X defined over complex numbers, $\mid mK_{X}\mid$ gives a birational rational map from X into a projective space.
We prove a subadjunction theorem which relates the multi-adjoint linear system of the ambient space and the linear system of the restricted bundle on a subvariety.
By means of analytic methods the quasi-projectivity of the moduli space of algebraically polarized varieties with a not necessarily reduced complex structure is proven including the case of non-uniruled polarized varieties.
We prove the invariance of plurigenera under smooth projective deformations in full generality. The proof is done by several estimates of singular hermitian metrics in terms of $L^{2}$-extension theorem of holomorphic sections.
We prove the invariance of plurigenera under smooth projective deformations of varieties with nonnegative Kodaira dimensions.