Deformation Invariance of Plurigenera
Hajime Tsuji
我们证明了plurigenes光滑射影变形下的不变性在充分的一般性。利用全纯截面的$L^{2}$ -扩张定理，利用奇异厄米度量的几种估计，给出了证明.
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.
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Invariance of plurigenera of varieties with nonngative Kodaira dimensions
我们证明了plurigenes的不变性下光滑的投影变形的品种与非负Kodaira尺寸。
We prove an invariance of plurigenera for some foliated surface pairs of general type.
Invariance of certain plurigenera for surfaces in mixed characteristics
本文证明了在离散赋值环上光滑的对数曲面的小平维数与某些多重亏格在形变下保持不变。
We construct smooth families of elliptic surface pairs with terminal singularities over a DVR of positive or mixed characteristic $(X,B)\to \mathrm{Spec}R$, such that $P_m(X_k,B_k)>P_m(X_K,B_K)$ for all sufficiently divisible $m>0$. In particular, this shows that invariance of all sufficiently divisible plurigenera does not follow from the MMP and Abundance Conjectures.
Aspects of deformation invariance of plurigenera of Kähler varieties
该研究结合准则与凯勒极小模型纲领，证明了凯勒族多重典范类等的多项形变不变性结果，并将广义极化对的相关不变性结论从射影族推广至莫伊谢佐恩族。
Invariance of plurigenera and good minimal models
本文将 Nakayama 关于多重亏格形变不变性的结果推广至正或混合特征 DVR 上的奇异对族，并证明了特定一般型簇好极小模型形变的多重亏格不变性及三维 Gorenstein 典范模型的有界性。
In this note, we survey some recent developments in birational geometry concerning the boundedness of algebraic varieties. We delineate a strategy to extend some of these results to the case of generalized pairs, first introduced by Birkar and Zhang, when the associated log canonical divisor is ample, and the volume is fixed. In this context, we show a version of deformation invariance of plurigenera for generalized pairs. We conclude by discussing an application to the boundedness of varieties of Kodaira dimension $κ(X)=\dim(X)-1$.
We show the invariance of plurigenera for generalized polarized pairs with abundant nef parts and generalized canonical singularities. This is obtained by investigating a type of newly introduced multiplier ideal sheaf which is of bimeromorphic nature.
On invariance of plurigenera for foliations on surfaces
我们表明，如果$(X_t,\mathcal{F}_t)_t$是一个家庭的叶理减少奇点的一个光滑的家庭的表面上，那么不变性的plurigenes持有足够大的$m$。另一方面，我们提供的例子上的结果失败，为小值的$m$。
This is the third paper in a series of work on weighted stable elliptic surfaces - elliptic fibrations with section and marked fibers weighted between zero and one. Motivated by Hassett's weighted pointed stable curves, we use the log minimal model program to construct compact moduli spaces parameterizing these objects. Moreoever, we show that the domain of weights admits a wall and chamber structure, we describe the induced wall crossing morphisms on the moduli spaces as the weight vector varies, and describe the surfaces that appear on the boundary of the moduli space. The main technical res…
This paper answers a question of Demailly whether a smooth family of nonsingular projective varieties admits the deformation invariance of plurigenera affirmatively, and proves this more generally for a flat family of varieties with only canonical singularities and uncountable ones therein being of general type and also two Chow-type lemmata on the structure of a family of projective complex analytic spaces.
Invariance of Plurigenera
证明了以下关于复属变形不变性的猜想。对于开单位圆盘上的紧致复流形的光滑射影全纯族，使得所有纤维都是一般型的，纤维的每一个复亏格都与纤维无关。证明使用了Nadel的乘子理想层，Skoda关于L2估计的理想生成的结果，以及Ohsawa-Takegoshi-Manivel关于L2的全纯顶度形式的扩张定理。
We prove that small deformations of a projective variety of general type are also projective varieties of general type, with the same plurigenera. Version 2: small changes in first half. Improved version of the second half is now a separate preprint (Seshadri's criterion and openness of projectivity). Version 3: Footnote corrects citation on p.4.
Canonical singular hermitian metrics on relative logcanonical bundles
这取代了0704.0566。证明了KLT对的射影族和KLT线丛的伴随线丛的对数多属不变性。证明使用了相对对数正则丛上的正则奇异厄米特度量。
On Pseudo-Effectivity and Volumes of Adjoint Classes in Kähler Families with Projective Central Fiber
本文研究了Kähler族中伴随类的伪有效性与体积的变形行为，证明了体积的局部不变性并验证了Siu的不变性猜想。
Deformation invariance of canonical nefness in smooth Kahler morphisms
本文证明在光滑Kähler态射中，典范丛的nef性具有形变不变性，即若某一纤维的典范丛nef，则所有纤维均nef，从而解决了Campana和Peternell提出的开性问题。
Kollar and Ruan proved symplectic deformation invariance for uniruledness of Kaehler manifolds. Zhiyu Tian proved the same for rational connectedness in dimension < 4. Kollar conjectured this in all dimensions. We prove Kollar's conjecture, as well as existence of a covering family of rational surfaces, for all Kaehler manifolds that are symplectically deformation equivalent to G/P or to a low degree complete intersection in such.
Deformation invariance of rational pairs
最近由Kollár和Kovács引入的有理对将有理奇点推广到对$(X,D)$。这里，$X$是一个正规簇，$D$是$X$的一个简化除子。有理数对的定义中不可或缺的是节俭归结的概念，也是由Kollár和Kovács定义的，为了使用有理数对，通常需要知道给定的归结是否节俭。在本文中，我们提出了几个基本的结果，有助于识别节俭的决议和分析他们的行为。我们还表明，一般超平面部分的理性对再次理性。1978年，Elkik证明了有理奇点是形变不变的。我们的主要结果是有理对定理的一个类似：给定一个平坦族$X\to S$和$X$上的一个Cartier因子$D$，如果光滑点$s\in S$上的纤维形成有理对，则$(X,D)$在纤维$X_s$附近也是有理的。
Birational invariance in logarithmic Gromov-Witten theory
Gromov-Witten不变量已经被构造为变形不变量，但它们在其他变换下的行为是微妙的。在本文中，我们证明了对数Gromov-Witten不变量在适当定义的对数修改下也是不变的。
Motivic and quantum invariance under stratified Mukai flops
对于$A_{n,k}, D_{2k+1}$型和$E_{6,I}$型分层向井触发器，证明了纤维积在Chow基模上诱导同构。与（标准）Mukai拖鞋相反，上积产品通常不被保存。对于$A_{n, 2}$、$D_5$和$E_{6, I}$触发器，通过对普通触发器的退化/变形，发现了量子修正。
A universal metric for the canonical bundle of a holomorphic family of projective algebraic manifolds
证明了紧致复代数流形的全纯族的典范丛带有一个具有非负曲率流的奇异Hermite度量，且中心纤维的典范丛的每个全纯截面关于这个度量都是L^2.当科的成员是一般型时，这一结果被Siu证明，并用于建立在这种情况下的多属的变形不变性。事实上，我们证明了我们的结果在一个更一般的设置光滑超曲面不一定正常的平凡丛在一个流形是斯坦以外的解析子品种。这样的设置首先由高山考虑。(In在一个家庭的情况下，正规丛是平凡的。）该方法的证明涉及适应最近的工作Paun。
Invariance de la Gamma-dimension pour certaines familles kählériennes de dimension 3
在这篇文章中，我们研究了Gamma维（定义在X是一个紧kähler流形）的形变不变性的一些性质。这个双有理不变量被定义为X的泛覆盖中的极大紧子簇的余维数。在曲面的情况下，变形不变性是Y. T.萧利用F. Campana et Q.张，我们解决了这种不变性的某些类型的凯勒家庭的3维。
Deformations, local freeness, and base change for higher Du Bois singularities
该研究证明严格高阶Du Bois奇点在小形变下不变，针对严格高阶Du Bois纤维的相对Du Bois复形建立基变换定理，展示1-Du Bois纤维的相关失效并推广局部自由性定理、证明Hodge数不变性。
Deformation of 2-step Nilmanifolds with Abelian Complex Structures
我们发展了零流形上阿贝尔不变复结构的形变理论，并证明了在这种情况下，Kuranishi过程保持不变性质。一个纯粹的代数条件的特点再次导致阿贝尔结构的变形，我们证明，这样的变形是通畅的。各种例子说明了由此产生的理论，以及在3个复杂的维度中可能的行为。
Deformation Openness of Big Fundamental Groups and Applications
本文证明了具有大复局部系统的光滑射影簇的大基本群性质在小形变下稳定，还研究了更一般的Γ-维数形变不变猜想，并发展相关技术得到伪Brody双曲性形变开性等应用。
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