Hajime Tsuji
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 $m\geq ν_{n}$.
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We describe examples showing the sharpness of Fujita's conjecture on adjoint bundles also in the general type case, and use these examples to formulate related bold conjectures on pluricanonical maps of varieties of general type.
Pluricanonical Geometry of Varieties Isogenous to a Product and Abelian Covers
研究同源于积的三次曲面的典范映射，证明当$p_g \ge 5$时4-典范映射为理性映射，并构造最大典范度的例子。
Given a fibration $f$ between two projective manifolds $X$ and $Y$, we discuss the effective generation of the higher direct images $R^{i}f_{\ast}(K^{m}_{X})$, where $K^{m}_{X}$ is the $m$-th tensor power of the canonical bundle of $X$. In particular, we answer two questions posed by Popa--Schnell in [PS14].
Given a fibration $f$ between two projective manifolds $X$ and $Y$, we provide a sufficient condition such that the direct images $f_{\ast}(K_{X/Y}\otimes L\otimes\mathscr{I}(f,\|L\|))$ is nef, where $L$ is a holomorphic line bundle with non-negative relative Iitaka dimension and $\mathscr{I}(f,\|L\|)$ is the relative asymptotic multiplier ideal sheaf.
We study pluricanonical systems on smooth projective varieties of positive Kodaira dimension, following the approach of Hacon-McKernan, Takayama and Tsuji succesfully used in the case of varieties of general type. We prove a uniformity result for the Iitaka fibration of smooth projective varieties of positive Kodaira dimension, provided that the base of the Iitaka fibration is not uniruled, the variation of the fibration is maximal, and the generic fiber has a good minimal model.
An invariant kernel for the pluricanonical system of a projective manifold of general type is introduced. Using this kernel we prove that the Yau volume form on a smooth projective variety has seminegative Ricci curvature. As a biproduct we prove the invariance of plurigenera for smooth projective deformations of manifolds of general type.
Meromorphic maps from ${\Bbb C}^{p}$ into semi-abelian varieties and general projective varieties
通过纤维积分降维法，将全纯曲线的Nevanlinna型结果推广到从${\Bbb C}^{p}$到射影簇的亚纯映射，包括Bloch定理、第二基本定理等。
We introduce a division formula on a possibly singular projective subvariety $X$ of complex projective space $\Pk^N$, which, e.g., provides explicit representations of solutions to various polynomial division problems on the affine part of $X$. Especially we consider a global effective version of the Brian\c con-Skoda-Huneke theorem.
We discuss two results about projective representations of fundamental groups of quasiprojective varieties. The first is a realization result which, under a nonresonance assumption, allows to realize such representations as monodromy representations of flat projective logarithmic connections. The second is a lifting result: any representation as above, after restriction to a Zariski open set and finite pull-back, can be lifted to a linear representation.
We provide supplements and open problems related to structure theorems for maximal rationally connected fibrations of certain positively curved projective varieties, including smooth projective varieties with semi-positive holomorphic sectional curvature, pseudo-effective tangent bundle, and nef anti-canonical divisor.
In the context of uniformisation problems, we study projective varieties with klt singularities whose cotangent sheaf admits a projectively flat structure over the smooth locus. Generalising work of Jahnke-Radloff, we show that torus quotients are the only klt varieties with semistable cotangent sheaf and extremal Chern classes. An analogous result for varieties with nef normalised cotangent sheaves follows.
On the minimal model program for projective varieties with pseudo-effective tangent sheaf
本文发展正规射影簇上伪有效层的理论，并通过运行极小模型计划，证明具有伪有效切层的射影klt簇可分解为Fano簇和Q-阿贝尔簇。
We characterize possible periodic subvarieties for surjective endomorphisms of complex abelian varieties in terms of the eigenvalues of the cohomological actions induced by the endomorphisms, extending previous work in this direction by Pink and Roessler. By applying our characterization to induced endomorphisms on Albanese varieties, we draw conclusions about the dynamics of surjective endomorphisms for a broad class of projective varieties. We also analyze several classes of surjective endomorphisms that are distinguished by properties of their cohomological actions.
In this paper, we study holomorphic curves satisfying the Fubini-Study derivative $\|f'(z)\|=O(|z|^σ)$ for some $σ>-1$ from the viewpoint of Nevanlinna theory
We obtain sufficient and necessary conditions (in terms of positive singular metrics on an associated line bundle) for a positive divisor $D$ on a projective algebraic variety $X$ to be attracting for a holomorphic map $f:X \mapsto X$.
Let X be an irreducible n-dimensional projective variety in CP^N with arbitrary singular locus. We prove that the L2-(p,1)-d-bar cohomology groups (with respect to the Fubini-Study metric) of the regular part of X are finite dimensional.
We give a characterization of the boundaries of holomorphic chains in complex projective space in terms of certain non-linear moment conditions. This extends previous work of the authors and complements results of Dolbeault and Henkin.
By the quantization condition compact quantizable Kaehler manifolds can be embedded into projective space. In this way they become projective varieties. The quantum Hilbert space of the Berezin-Toeplitz quantization (and of the geometric quantization) is the projective coordinate ring of the embedded manifold. This allows for generalization to the case of singular varieties. The set-up is explained in the first part of the contribution. The second part of the contribution is of tutorial nature. Necessary notions, concepts, and results of algebraic geometry appearing in this approach to quantiz…
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