On the String-Theoretic Euler Number of a Class of Absolutely Isolated Singularities
Dimitrios I. Dais
备注：
LateX 2e, 27 pages, 4 eps figures. Revised version V2 (October 2001) corrects some arithmetical inaccuracies (pointed out by N. Kakimi, concering the discrepancy coefficients) of V1, and minor misprints of the published version
An explicit computation of the so-called string-theoretic E-function of a normal complex variety X with at most log-terminal singularities can be achieved by constructing one snc-desingularization of X, accompanied with the intersection graph of the exceptional prime divisors, and with the precise knowledge of their structure. In the present paper, it is shown that this is feasible for the case in which X is the underlying space of a class of absolutely isolated singularities (including both usual A_{n}-singularities and Fermat singularities of arbitrary dimension). As byproduct of the exact evaluation of e_{str}(X), for this class of singularities, one gets (in contrast to the expectations of V1!) counterexamples to a conjecture of Batyrev concerning the boundedness of the string-theoretic index. Finally, the string-theoretic Euler number is also computed for global complete intersections in P^{N} with prescribed singularities of the above type.
Flops and Hilbert schemes of space curve singularities
New High Energy Theory Center - Serrin Building, Rutgers, The State University Of New Jersey（新高能理论中心-塞林楼，罗格斯大学（新泽西州立大学））；Kavli IPMU (WPI), UTIAS, The University of Tokyo（卡弗里宇宙物理起源研究所（世界顶尖科学中心），东京大学信息科学与技术研究院）
Euler numbers of Hilbert schemes of points on simple surface singularities and quantum dimensions of standard modules of quantum affine algebras
Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo（东京大学宇宙物理数学研究所（WPI））；Research Institute for Mathematical Sciences, Kyoto University（京都大学数理解析研究所）
We show a coincidence of index of rigidity of differential equations with irregular singularities on a compact Riemann surface and Euler characteristic of the associated spectral curves which are recently called irregular spectral curves. Also we present a comparison of local invariants, so called Milnor formula which links the Komatsu-Malgrange irregularity of differential equations and Milnor number of the spectral curves.
A Direct Algorithm to Compute the Topological Euler Characteristic and Chern-Schwartz-MacPherson Class of Projective Complete Intersection Varieties
设$V$是特征为零的代数闭域上$\mathbb{P}^n$的可能奇异的概型论完全交子概型.利用Fullwood（“On Milnor classes via invariants of singular subschemes”，Journal of Singularities）的最新结果，我们发展了一个计算$V$的Chern-Schwartz-MacPherson类和欧拉示性数的算法.该算法补充了现有的算法，提供性能改进的计算的陈施瓦茨-麦克弗森类和欧拉示性数的某些类型的完全相交的子计划的$\mathbb{P}^n$。
This article and its successor concern the topology of real isolated hypersurface singularities. We prove that after attaching a certain number of handles the real Milnor fibres become contractible, with each handle corresponding to a critical point of a morsification; in particular one recovers the classical formula of Khimshiashvili for the Euler characteristic of the Milnor fibres. We then give sufficient conditions for having that the integer homology groups of the real Milnor fibres are isomorphic to the homology groups of a bouquet of spheres. This is followed by a discussion on real van…
