Pure Log Terminal Blow-Ups

The existence of a pure log terminal blow-up for a log terminal singularity and a criterion for a singularity to be weakly exceptional are proved.     

Log canonical foliation singularities on surfaces

We give a classification of the dual graphs of the exceptional divisors on the minimal resolutions of log canonical foliation singularities on surfaces. As an application, we show the set of foliated minimal log discrepancies for foliated surface triples satisfies the ascending chain condition and a Grauert–Riemenschneider–type vanishing theorem for foliated surfaces with special log canonical foliation singularities.     

Log Structures on Generalized Semi-Stable Varieties

In this paper, a class of morphisms which have a kind of singularity weaker than normal crossing is considered. We construct the obstruction such that the so-called semi-stable log structures exists if and only if the obstruction vanishes. In the case of no power, if the obstruction vanishes, then the semi-stable log structure is unique up to a unique isomorphism. So we obtain a kind of canonical structure on this family of morphisms.     

Zeta Functions for Curves and Log Canonical Models

The topological zeta function and Igusa's local zeta functionare respectively a geometrical invariant associated to a complexpolynomial f and an arithmetical invariant associated to a polynomialf over a p-adic field. When f is a polynomial in two variables we prove a formula forboth zeta functions in terms of the so-called log canonicalmodel of f^-1{0} in A². This result yields moreover a conceptualexplanation for a known cancellation property of candidate polesfor these zeta functions. Also in the formula for Igusa's localzeta function appears a remarkable non-symmetric ‘q-deformation’of the intersection matrix of the minimal resolution of a Hirzebruch-Jungsingularity. 1991 Mathematics Subject Classification: 32S5011S80 14E30 (14G20)     

基于海量网站日志数据的房地产需求指数研究

网络日志数据作为亿万消费者的意图数据库,为研究消费者需求波动提供了有效的量化指标,研究以北京市二手房为例,首先构建网站浏览日志数据与房地产成交量的关联模型,根据用户购房意图对网站进行分类,以不同类型房产网站的浏览次数(PV)、用户数(UV)等数据衡量购房者的关注及需求波动,构建房产成交量的先行、一致和滞后指数并对其关系进行检验,构建的房产指数是对现有指标体系的补充,为房地产开发商、普通购房者、政府相关管理部门提供决策指导和参考依据.     

The set of toric minimal log discrepancies

We describe the set of minimal log discrepancies of toric log varieties, and study its accumulation points. This work is supported by a 21st Century COE Kyoto Mathematics Fellowship, and a JSPS Grant-in-Aid No 17740011.     

Log canonical thresholds of divisors on Grassmannians

Let L be the Plücker line bundle on the Grassmannian. Given D ∈ |kL|, we show that the log canonical threshold of D is at least . The main ingredients of the proof are Kapranov's result on the derived category of coherent sheaves on the Grassmannian, Nadel's vanishing theorem for multiplier ideal sheaves, and Demailly's vanishing theorem for vector bundles.     

A Re‐Examination of Sharpe's Ratio for Log‐Normal Prices

The purpose of this paper is to examine the exact properties of Sharpe's ratio when prices are log‐normal. Depending on the definition of returns, different expressions are formed for unbiased estimators of Sharpe's ratio.     

Rational, Log Canonical, Du Bois Singularities II: Kodaira Vanishing and Small Deformations

Kollár's conjecture, that log canonical singularities are Du Bois, is proved in the case of Cohen–Macaulay 3-folds. This in turn is used to derive Kodaira vanishing for this class of varieties. Finally it is proved that small deformations of Du Bois singularities are again Du Bois.     

对数收益率的偏斜Logistic分布与VaR估计

本文通过直方图和Q-Q图的直观方法展示了上证指数和深证指数的对数收益率具有尖峰厚尾和偏斜的分布特征,利用Shapiro-Wilk正态性检验和Kolmogorov-Smirnov检验等方法检验了对数收益率的分布与正态分布有显著性差异,并以较大的概率水平接受了对数收益率服从偏斜Logistic分布,同时给出了基于偏斜Logistic分布的VaR风险量的估计,结果显示上证指数的风险小于深证指数的风险。     

Log Canonical Thresholds of Del Pezzo Surfaces

We study global log canonical thresholds of del Pezzo surfaces. All varieties are assumed to be defined over . Received: May 2007 Revision: October 2007 Accepted: April 2008     

Adjoint Linear Systems on Normal Log Surfaces

We prove a Reider type theorem for separating any cluster by an adjoint system to a pseudoeffective divisor on a normal surface. As a corollary we get a Reider type theorem for adjoint linear systems (to a nef Q-divisor) on normal log surfaces. This theorem is new even for smooth surfaces.     

Log geometry and exploded manifolds

Log Gromov-Witten invariants have recently been defined separately by Gross and Siebert and Abramovich and Chen. This paper provides a dictionary between log geometry and holomorphic exploded manifolds in order to compare Gromov-Witten invariants defined using exploded manifolds or log schemes. The gluing formula for Gromov-Witten invariants of exploded manifolds suggests an approach to proving analogous gluing formulas for log Gromov-Witten invariants.     

Log canonical thresholds of del Pezzo surfaces in characteristic p

The global log canonical threshold of each non-singular complex del Pezzo surface was computed by Cheltsov. The proof used Kollár–Shokurov’s connectedness principle and other results relying on vanishing theorems of Kodaira type, not known to be true in finite characteristic. We compute the global log canonical threshold of non-singular del Pezzo surfaces over an algebraically closed field. We give algebraic proofs of results previously known only in characteristic 0. Instead of using of the connectedness principle we introduce a new technique based on a classification of curves of low degree. As an application we conclude that non-singular del Pezzo surfaces in finite characteristic of degree lower or equal than 4 are K-semistable.     

Log pairs on hypersurfaces of degreeN in {N{\text{ in }}\mathbb{P}^N

The objective of this paper is to study the birational structure of smooth hypersurfaces of degreeN in by examining properties of moving log pairs on them. Translated fromMatematicheskie Zametki, Vol. 68, No. 1, pp 131–138, July, 2000.     

原木随机存贮策略的最优化问题

本主要介绍原木经销商在周期内原木变价销售情况下的最佳期初贮存量的决策方法，在建立期望机会成本的数学模型基础上，探讨原木随机存贮策略的最优化问题。     

Kawamata-Viehweg vanishing fails for log del Pezzo surfaces in characteristic 3

We construct a klt del Pezzo surface in characteristic three violating the Kawamata-Viehweg vanishing theorem. As a consequence we show that there exists a Kawamata log terminal threefold singularity which is not Cohen-Macaulay in characteristic three.     

On log canonical divisors that are log quasi-numerically positive

Let (X Δ) be a four-dimensional log variety that is projective over the field of complex numbers. Assume that (X, Δ) is not Kawamata log terminal (klt) but divisorial log terminal (dlt). First we introduce the notion of “log quasi-numerically positive”, by relaxing that of “numerically positive”. Next we prove that, if the log canonical divisorK _X+Δ is log quasi-numerically positive on (X, Δ) then it is semi-ample.     

Log del Pezzo surfaces with not small fractional indices

For a log del Pezzo surface S, the fractional index is the maximum of r with which can be written as r times some Cartier divisor. We classify all the log del Pezzo surfaces S with , after the technique of Nakayama.