The structure of polarized varieties

首席研究员Fujita研究了#-极小模型理论和伴随丛理论之间的关系。他进一步研究了三次曲面在P^3的Cremona变换下的行为。研究者石井研究了例外超曲面的奇异性，并证明了只有1000多个权值才能给出例外超曲面。她进一步分类了所有Brieskorn类型的三维异常奇点。她研究了许多有趣的性质的一套可能的价值观不变K^2的表面奇性，并进一步研究了之间的关系的积累点的一套K^2的循环商奇性和积累点，相应的连续分数。她还指出，对于一个给定的奇点，存在一个极大流形，通过该极大流形，光滑流形的每个满射态射因子，她通过有理曲线的存在性来表征这种流形，并研究了直积，商和函性等性质。研究员Futaki表明，对于复线丛L及其Chern类（Hodge类），如果自同构群的作用提升到L，则Futaki特征标提升到自同构群的特征标。他还给出了一个明确的积分表达式，这电梯，并表明，它可以应用，交出马渊的K-研究者Tsuji利用奇异Hermitian度量理论证明了多属的形变不变性;研究者Nakayama系统地研究了原木形变族上的混合Hodge结构;研究者Kawachi将正规曲面上的Reider型结果推广到原木的情形Minagawa研究员研究了弱Fano 3-folds的光滑性准则，并表明Q-因子性是足够的。他还发现了一个没有Q因子的非光滑的例子。

The head investigator Fujita has studied the relation between the theory of #-minimal models and the theory of adjoint bundles. He further studied the behavior of cubic surfaces under the Cremona transformations of P^3.Investigator Ishii has studied the exceptional hypersurface singularities and showed that there are only finitely many weights which give exceptional ones. 'She further classified all the 3-dimensional exceptional singularities of Brieskorn type. She studied many interesting properties of the set of possible values of the invariant K^2 of surface singularities, and further studied the relation between the accumulation points of the set of K^2 of cyclic quotient singularities and the accumulation points, of the corresponding continued fractions. She showed also that, for a given singularity, there exists a maximal manifold through which every surjective morphism from a smooth manifold factors, and she characterized such manifold by the existence of rational curves, and studied the properties such as direct product, quotient and functoriality.Investigator Futaki has showed that for a complex line bundle L together with its Chern class which is a Hodge class, if the action of the automorphism group lifts to L, then the Futaki character lifts to a character of the automorphism group. He gave also an explicit integral expression of this lift, and showed that it can be applied, to yield Mabuchi's K-energy and Ding's functional.Investigator Tsuji has showed the deformation invariance of plurigenera by applying the theory of singular Hermitian metrics.Investigator Nakayama has studied systematically mixed Hodge structures on log deformation families.Investigator Kawachi has generalized results of Reider type on normal surfaces to cases of log algebraic surfaces.Investigator Minagawa has studied criterions of smoothability of weak Fano 3-folds, and showed that Q-factoriality is sufficient. He also found an example of non-smoothable ones without Q-factoriality.