On effective non-vanishing and base-point-freeness
Yujiro Kawamata
设$X$是完全正规簇，$B$是$X$上的有效$\mathbb{R}$ -因子，$D$是$X$上的Cartier因子.假设对$(X, B)$是日志终端。在低维情况下，我们考虑了是否为$H^0(X, D) \ne 0$的问题，得到了一些结果.
Let $X$ be a complete normal variety, $B$ an effective $\mathbb{R}$-divisor on $X$, and $D$ a Cartier divisor on $X$. Assume that the pair $(X, B)$ is log terminal. We consider the problem whether $H^0(X, D) \ne 0$ and obtain some results in lower dimensions.
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On vanishing and torsion-freeness results for adjoint pairs
本文证明了满足相对丰度与数值有效条件的伴随对高次直接像的消失与无挠性定理，并应用于一般消失与弱正性。
Strong non-vanishing of cohomologies and strong non-freeness of adjoint line bundles on $n$-Raynaud surfaces
本文定义 n-Tango 曲线与 n-Raynaud 曲面，分析其病态上同调及伴随线丛性质，并据此简洁否定正特征曲面情形的 Fujita 猜想。
We prove the injectivity and vanishing theorem for R-Hodge modules and R-divisors over projective varieties, extending the results for rational Hodge modules and integral divisors in \cite{Wu15}. In particular, the injectivity generalizes the fundamental injectivity of Esnault-Viehweg for normal crossing Q-divisors, while the vanishing generalizes Kawamata-Viehweg vanishing for Q-divisors. As a main application, we also deduce a Fujita-type freeness result for R-Hodge modules in the normal crossing case.
Kollár's package for polystable locally abelian parabolic Higgs bundles
本文将Kollár工具包推广到带乘子理想扭转的多稳定局部阿贝尔抛物Higgs丛，统一复几何中的相关定理，并推出高正像层的弱正性与一般消灭性质。
In this note, we study base point freeness up to taking p-power, which we will call p-power freeness. We first establish some criteria for p-power freeness as analogues of criteria for semi-ampleness. We then apply these results to three-dimensional birational geometry.
Towards generic base-point-freeness for hyperkähler manifolds of generalized Kummer type
本文研究广义 Kummer 型超凯勒流形上大且 nef 线丛的无基点性，证明了在低维及可除性为 1 时，模空间中一般极化无基点。
Let $X$ be a smooth projective variety of dimension $5$ and $L$ be an ample line bundle on $X$. We show that $|K_X + 6L|$ is base-point free.
Effective base point freeness on normal surfaces
给出了带边界法曲面上伴随丛整体生成的新的有效判据。我们可以在对数终端奇点上使不变量δ更小一点，然后我们可以证明我以前的论文“alg-geom/9612018”中描述的定理作为推论。
For a polarized abelian variety $(X,L)$, Z. Jiang and G. Pareschi introduce an invariant $β(X,L)$, called the basepoint-freeness threshold. Using this invariant, we show that a general polarized abelian variety $(X,L)$ of dimension $g$ is projectively normal if $χ(L) \geq 2^{2g-1}$ and the type of $L$ is not $(2,4,\dots,4)$. This bound is sharp since it is known that any polarized abelian variety of type $(2,4,\dots,4)$ is not projectively normal. We also give an application of $β(X,L)$ to the Infinitesimal Torelli Theorem for $Y \in |L|$.
Dimension estimates for Hilbert schemes and effective base point freeness on moduli spaces of vector bundles on curves
我们得到了曲线上向量丛模空间上多θ线丛的整体生成的有效结果。主要成分是一个独立的结果，给出了一个上界的Hilbert计划的维数的相干分量的一个给定的向量丛。
Effective freeness of adjoint line bundles
本文建立了复维数紧复射影流形$n$上伴随线丛的基点自由度的一个新的Fujita型有效界。我们得到的界（近似）与Fujita给出的线性界仅相差$n$的立方根的一个因子。作为应用，给出了一个新的多重正则嵌入的有效性说明。
On base point freeness for rank one foliations
本文研究了秩为一的叶形在Q-因子有限准正则三重域上的基点自由性，并在数值上平凡的情况下证明了其丰盈性。
We show that Ambro-Kawamata's non-vanishing conjecture holds true for a quasi-smooth WCI X which is Fano or Calabi-Yau, i.e. we prove that, if H is an ample Cartier divisor on X, then |H| is not empty. If X is smooth, we further show that the general element of |H| is smooth. We then verify Ambro-Kawamata's conjecture for any quasi-smooth weighted hypersurface. We also verify Fujita's freeness conjecture for a Gorenstein quasi-smooth weighted hypersurface. For the proofs, we introduce the arithmetic notion of regular pairs and enlighten some interesting connection with the Frobenius coin probl…
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。
We prove that if $(X,A+B)$ is a pair defined over an algebraically closed field of positive characteristic such that $(X,B)$ is strongly $F$-regular, $A$ is ample and $K_X+A+B$ is strictly nef, then $K_X+A+B$ is ample. Similarly, we prove that for a log pair $(X,A+B)$ with $A$ being ample and $B$ effective, $K_X+A+B$ is big if it is nef and of maximal nef dimension. As an application, we establish a rationality theorem for the nef threshold and various results towards the minimal model program in dimension three in positive characteristic.
Effective base point freeness on a normal surface
这处理了具有边界的法向曲面上的伴随丛的基点自由性。这是Ein-Lazarsfeld-Masek定理和Kawachi-Masek定理的非相对版本的推广。
Freeness of Pluricanonical Linear System on Smooth Minimal n-folds of General Type
本文证明了一般型光滑极小n维簇上$|\frac{n^2+n+2}{2}K_X|$无基点，并给出Fujita无基点猜想在nef且大除数情形下的界限，同时证明了$K_X+mB$的基点集包含于增广基轨迹。
On freeness theorem of the adjoint bundle on a normal surface
我们将Reider的自由度准则推广到特征为0的法向曲面。设Y是一个法向曲面。设D是Y上的nef因子，使得K_Y+D是Cartier因子.设x是Y上的一点。如果x是一个基点，|K_Y+D|且D^2>δ_x（δ_x由x决定，δ_x <= 4），则存在Y上通过x的非零有效因子E，使得0 <= DE <= δ_x /2，DE - δ_x /4 <= E^2 <=（DE）^2 / D^2，若DE=0，则E^2 < 0。
Effective generic freeness and applications to local cohomology
该研究探讨诺特整环上有限生成代数模的一般自由性，证明光滑代数下局部上同调模的一般自由性，并借助格罗比纳基理论给出显式判定的有效方法。
Let X be a smooth complex projective variety of dimension n. We prove bounds on Fujita's basepoint freeness conjecture that grow as nloglog(n).
Continuous CM-regularity and generic vanishing
本文研究极化不规则光滑射影簇上无挠凝聚层的连续 CM-正则性，肯定回答了 Mustopa 关于连续 1-正则层是否为 GV 的问题，推广该正则性至 Q-扭曲丛的实值函数，并给出合系推论。
Effective base point free theorem for log canonical pairs II--Angehrn--Siu type theorems--
证明了对数典型对的Angehrn-Siu型有效基点自由性和点分离性。
In this paper we discuss an obstruction to the integral Hodge conjecture, which arises from certain behavior of vanishing cycles. This allows us to construct new counter-examples to the integral Hodge conjecture. One typical such counter-example is the product of a very general hypersurface of odd dimension and an Enriques surface. Our approach generalizes the degeneration argument of Benoist-Ottem.
We study the relationship between positivity of line bundles restricted to complete intersection subvarieties and the vanishing of higher cohomology groups. Based on this connection we prove generalizations of the vanishing theorems of Kawamata-Viehweg and Fujita that are valid for not necessarily big line bundles.
Vanishing theorems and universal coverings of projective varieties
本文给出了复射影簇上负向量丛的第一上同调为零的一个新的证明，如果丛的秩小于基的维数。类似的论证被应用于复射影簇的泛覆盖上的全纯函数的构造。
Explicit non-free tensors
本文通过几何不变量理论和矩多面体方法，为每个n≥3显式构造了C^n⊗C^n⊗C^n中的非自由张量，解决了此前缺乏显式非自由张量的问题，并确立了非自由张量的存在性。
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