共查询到20条相似文献,搜索用时 0 毫秒
1.
Jan Stevens 《Mathematische Nachrichten》2009,282(8):1195-1215
We give explicit examples of Gorenstein surface singularities with integral homology sphere link, which are not complete intersections. Their existence was shown by Luengo–Velasco, Melle–Hernández and Némethi, thereby providing counterexamples to the universal abelian covering conjecture of Neumann and Wahl (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
2.
Taro HAYASHI 《数学年刊B辑(英文版)》2023,44(1):99-162
The quotient space of a K3 surface by a finite group is an Enriques surface or a rational surface if it is smooth. Finite groups where the quotient space are Enriques surfaces are known. In this paper, by analyzing effective divisors on smooth rational surfaces, the author will study finite groups which act faithfully on K3 surfaces such that the quotient space are smooth. In particular, he will completely determine effective divisors on Hirzebruch surfaces such that there is a finite Abelian co... 相似文献
3.
Tomohiro Okuma 《Transactions of the American Mathematical Society》2008,360(12):6643-6659
We prove a formula for the geometric genus of splice-quotient singularities (in the sense of Neumann and Wahl). This formula enables us to compute the invariant from the resolution graph; in fact, it reduces the computation to that for splice-quotient singularities with smaller resolution graphs. We also discuss the dimension of the first cohomology groups of certain invertible sheaves on a resolution of a splice-quotient singularity.
4.
Tomohiro Okuma 《Mathematische Annalen》2006,334(4):753-773
Every normal complex surface singularity with -homology sphere link has a universal abelian cover. It has been conjectured by Neumann and Wahl that the universal abelian
cover of a rational or minimally elliptic singularity is a complete intersection singularity defined by a system of ``splice
diagram equations'. In this paper we introduce a Neumann-Wahl system, which is an analogue of the system of splice diagram
equations, and prove the following.
If (X, o) is a rational or minimally elliptic singularity, then its universal abelian cover (Y, o) is an equisingular deformation of an isolated complete intersection singularity (Y0, o) defined by a Neumann-Wahl system. Furthermore, if G denotes the Galois group of the covering Y → X, then G also acts on Y0 and X is an equisingular deformation of the quotient Y0/G.
Dedicated to Professor Jonathan Wahl on his sixtieth birthday.
This research was partially supported by the Grant-in-Aid for Young Scientists (B), The Ministry of Education, Culture, Sports,
Science and Technology, Japan. 相似文献
5.
We discuss the bi-Lipschitz geometry of an isolated singular point of a complex surface with particular emphasis on when it
is metrically conical.
相似文献
6.
Tomohiro Okuma 《Mathematische Nachrichten》2015,288(2-3):343-352
From a resolution graph with certain conditions, Neumann and Wahl constructed an equisingular family of surface singularities called splice quotients. For this class some fundamental analytic invariants have been computed from their resolution graph. In this paper we give a method to compute the multiplicity of an abelian covering of a splice quotient from its resolution graph and the Galois group. 相似文献
7.
D. A. Stepanov 《Proceedings of the American Mathematical Society》2008,136(8):2647-2654
It is well known that the exceptional set in a resolution of a rational surface singularity is a tree of rational curves. We generalize the combinatoric part of this statement to higher dimensions and show that the highest cohomologies of the dual complex associated to a resolution of an isolated rational singularity vanish. We also prove that the dual complex associated to a resolution of an isolated hypersurface singularity is simply connected. As a consequence, we show that the dual complex associated to a resolution of a 3-dimensional Gorenstein terminal singularity has the homotopy type of a point.
8.
Ben Wormleighton 《代数通讯》2020,48(1):119-140
AbstractThe Hilbert series of a polarized algebraic variety (X, D) is a powerful invariant that, while it captures some features of the geometry of (X, D) precisely, often cannot recover much information about its singular locus. This work explores the extent to which the Hilbert series of an orbifold del Pezzo surface fails to pin down its singular locus, which provides nonexistence results describing when there are no orbifold del Pezzo surfaces with a given Hilbert series, supplies bounds on the number of singularities on such surfaces, and has applications to the combinatorics of lattice polytopes in the toric case. 相似文献
9.
Lucio Guerra 《Annali di Matematica Pura ed Applicata》2006,185(3):319-335
We describe the moduli spaces of morphisms between polarized complex abelian varieties. The discrete invariants, derived from
a Poincaré decomposition of morphisms, are the types of polarizations and of lattice homomorphisms occurring in the decomposition.
For a given type of morphisms the moduli variety is irreducible, and is obtained from a product of Siegel spaces modulo the
action of a discrete group.
Mathematics Subject Classification (2000) 14K20 相似文献
10.
Trond Stlen Gustavsen 《Mathematische Nachrichten》2006,279(11):1185-1194
We prove dimension formulas for the cotangent spaces T 1 and T 2 for a class of rational surface singularities by calculating a correction term in the general dimension formulas. We get that it is zero if the dual graph of the rational surface singularity X does not contain a particular type of configurations, and this generalizes a result of Theo de Jong stating that the correction term c (X ) is zero for rational determinantal surface singularities. In particular our result implies that c (X ) is zero for Riemenschneiders quasi‐determinantal rational surface singularities, and this also generalizes results for quotient singularities. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
11.
Summary The aim of this Letter is to show that the singularities of integrable Hamiltonian systems, besides being important for such
systems themselves, also have many applications in the study of near-integrable systems. In particular, we will show how they
are related to Kolmogorov’s nondegeneracy condition (in the famous KAM theorem), the Poincaré-Melnikov function and its generalizations,
topological entropy, and nonintegrability criteria. 相似文献
12.
13.
We show that an infinite cyclic covering space M′ of a PD
n
-complex M is a PD
n-1-complex if and only if χ(M) = 0, M′ is homotopy equivalent to a complex with finite [(n−1)/2]-skeleton and π1(M′) is finitely presentable. This is best possible in terms of minimal finiteness assumptions on the covering space. We give
also a corresponding result for covering spaces M
ν with covering group a PD
r
-group under a slightly stricter finiteness condition.
相似文献
14.
Let S be a smooth, minimal rational surface. The geometry of the Severi variety parametrising irreducible, rational curves in a given linear system on S is studied. The results obtained are applied to enumerative geometry, in combination with ideas from Quantum Cohomology. Formulas enumerating rational curves are found, some of which generalised Kontsevich's formula for plane curves. 相似文献
15.
Rasoul Ahangari Maleki 《代数通讯》2013,41(8):3438-3452
Koszul modules over Noetherian local rings R were introduced by Herzog and Iyengar and they possess good homological properties, for instance their Poincaré series is rational. It is an interesting problem to characterize classes of Koszul modules. Following the idea traced by Avramov, Iyengar, and Sega, we take advantage of the existence of special filtration on R for proving that large classes of R-modules over Koszul rings are Koszul modules. By using this tool we reprove and extend some results obtained by Fitzgerald. 相似文献
16.
17.
We study special polynomials used to represent rational solutions of the hierarchy of the second Painlevé equation. We find
several recursion relations satisfied by these polynomials. In particular, we obtain a differential-difference relation that
allows finding any polynomial recursively. This relation is an analogue of the Toda chain equations.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 153, No. 1, pp. 58–67, October, 2007. 相似文献
18.
19.
Many works have investigated the problem of reparameterizing rational B~zier curves or surfaces via MSbius transformation to adjust their parametric distribution as well as weights, such that the maximal ratio of weights becomes smallerthat some algebraic and computational properties of the curves or surfaces can be improved in a way. However, it is an indication of veracity and optimization of the reparameterization to do prior to judge whether the maximal ratio of weights reaches minimum, and verify the new weights after MSbius transfor- mation. What's more the users of computer aided design softwares may require some guidelines for designing rational B6zier curves or surfaces with the smallest ratio of weights. In this paper we present the necessary and sufficient conditions that the maximal ratio of weights of the curves or surfaces reaches minimum and also describe it by using weights succinctly and straightway. The weights being satisfied these conditions are called being in the stable state. Applying such conditions, any giving rational B6zier curve or surface can automatically be adjusted to come into the stable state by CAD system, that is, the curve or surface possesses its optimal para- metric distribution. Finally, we give some numerical examples for demonstrating our results in important applications of judging the stable state of weights of the curves or surfaces and designing rational B6zier surfaces with compact derivative bounds. 相似文献
20.
Peter A. Clarkson David Gómez-Ullate Yves Grandati Robert Milson 《Studies in Applied Mathematics》2020,144(3):357-385
This paper focuses on the construction of rational solutions for the -Painlevé system, also called the Noumi-Yamada system, which are considered the higher order generalizations of PIV. In this even case, we introduce a method to construct the rational solutions based on cyclic dressing chains of Schrödinger operators with potentials in the class of rational extensions of the harmonic oscillator. Each potential in the chain can be indexed by a single Maya diagram and expressed in terms of a Wronskian determinant whose entries are Hermite polynomials. We introduce the notion of cyclic Maya diagrams and characterize them for any possible period, using the concepts of genus and interlacing. The resulting classes of solutions can be expressed in terms of special polynomials that generalize the families of generalized Hermite, generalized Okamoto, and Umemura polynomials, showing that they are particular cases of a larger family. 相似文献