共查询到20条相似文献，搜索用时 15 毫秒
1.
In this paper we solve the problemof desingularization of an absolutely isolatedsingularity of a differential equation, including thedicritical case. As an application, we prove thefiniteness of the number of dicritical points in theblowing up tree of an absolutely isolated singularity. 相似文献
2.
We generalize some results about the graded Milnor algebras of projective hypersurfaces with isolated singularities to the more general case of an almost complete intersection ideal J of dimension one. When the saturation I of J is a complete intersection, we get formulas for some invariants. Examples of hypersurfaces V: f = 0 in ?n whose Jacobian ideals J satisfy this property and with nontrivial Alexander polynomials are given in any dimension. A Lefschetz property for the graded quotient I/J is proved for n = 2 and a counterexample due to A. Conca is given for such a property when n = 3. 相似文献
3.
Daniel Panazzolo 《Acta Mathematica》2006,197(2):167-289
Let χ be an analytic vector field defined in a real-analytic manifold of dimension three. We prove that all the singularities of
χ can be made elementary by a finite number of blowing-ups in the ambient space.
This work has been partially supported by the CNPq/Brasil Grant 205904/2003-5 and Fapesp Grant 02/03769-9. 相似文献
4.
We prove that Lefschetz fibrations admitting a section of square cannot be decomposed as fiber sums. In particular, Lefschetz fibrations on symplectic 4-manifolds found by Donaldson are indecomposable. This observation also shows that symplectic Lefschetz fibrations are not necessarily fiber sums of holomorphic ones.
5.
Burak Ozbagci Andrá s I. Stipsicz 《Proceedings of the American Mathematical Society》2000,128(10):3125-3128
We construct noncomplex smooth 4-manifolds which admit genus-2 Lefschetz fibrations over . The fibrations are necessarily hyperelliptic, and the resulting 4-manifolds are not even homotopy equivalent to complex surfaces. Furthermore, these examples show that fiber sums of holomorphic Lefschetz fibrations do not necessarily admit complex structures.
6.
We address the geography problem of relatively minimal Lefschetz fibrations over surfaces of nonzero genus and prove that if the fiber-genus of the fibration is positive, then (equivalently, ) holds for those symplectic 4-manifolds. A useful characterization of minimality of such symplectic 4-manifolds is also proved.
7.
Mustafa Korkmaz Burak Ozbagci 《Proceedings of the American Mathematical Society》2001,129(5):1545-1549
There exists a (relatively minimal) genus Lefschetz fibration with only one singular fiber over a closed (Riemann) surface of genus iff and . The singular fiber can be chosen to be reducible or irreducible. Other results are that every Dehn twist on a closed surface of genus at least three is a product of two commutators and no Dehn twist on any closed surface is equal to a single commutator.
8.
We consider real analytic involutive structures 𝒱, of co-rank one, defined on a real analytic paracompact orientable manifold M. To each such structure we associate certain connected subsets of M which we call the level sets of 𝒱. We prove that analytic regularity propagates along them. With a further assumption on the level sets of 𝒱 we characterize the global analytic hypoellipticity of a differential operator naturally associated to 𝒱. As an application we study a case of tube structures. 相似文献
9.
Fedor A. Bogomolov Paolo Cascini Bruno de Oliveira 《Central European Journal of Mathematics》2006,4(2):194-208
We prove that any finite set of n-dimensional isolated algebraic singularities can be afforded on a simply connected projective
variety.
The first author was partially supported by NSF grant DMS-01591 and the third author was partially supported by NSF grant
DMS-03693 相似文献
10.
András I. Stipsicz 《Acta Mathematica Hungarica》2002,95(4):299-307
Using the theory of Lefschetz fibrations and recent advances in mapping class group theory, surface bundles over surfaces with nonzero signature and small base genus are constructed. In particular, a genus-5 fibration over the surface of genus 26 with nonzero signature is given –- improving former results on the possible base genera for surface bundles over surfaces with nonzero signature. 相似文献
11.
Naoyuki Monden 《Topology and its Applications》2012,159(4):1085-1091
We give new upper bounds on the stable commutator lengths of Dehn twists in mapping class groups and new lower bounds on the stable commutator lengths of Dehn twists in hyperelliptic mapping class groups. In particular, we show that the stable commutator lengths of Dehn twists about a nonseparating and a separating curve on an oriented closed surface of genus 2 are not equal to each other. 相似文献
12.
In this article, we provide a complete list of simple isolated Cohen–Macaulay codimension 2 singularities together with a list of adjacencies which is complete in the case of fat point and space curve singularities. 相似文献
13.
14.
For a symplectic manifold(M~(2n), ω) without boundary(not necessarily compact), we prove Poincaré type duality in filtered cohomology rings of differential forms on M, and we use this result to obtain duality between(d + d~Λ)-and dd~Λ-cohomologies. 相似文献
15.
Javier Fernandez 《Proceedings of the American Mathematical Society》2006,134(9):2511-2520
We construct a polarized Hodge structure on the primitive part of Chen and Ruan's orbifold cohomology for projective -orbifolds satisfying a ``Hard Lefschetz Condition'. Furthermore, the total cohomology forms a mixed Hodge structure that is polarized by every element of the Kähler cone of . Using results of Cattani-Kaplan-Schmid this implies the existence of an abstract polarized variation of Hodge structure on the complexified Kähler cone of .
This construction should be considered as the analogue of the abstract polarized variation of Hodge structure that can be attached to the singular cohomology of a crepant resolution of , in light of the conjectural correspondence between the (quantum) orbifold cohomology and the (quantum) cohomology of a crepant resolution.
16.
The structure of a Lie superalgebra is defined on the space of multiderivations of a commutative algebra. This structure is used to define some cohomology algebra of Poisson structure. It is shown that when a commutative algebra is an algebra of C
-functions on the C
-manifold, the cohomology algebra of Poisson structure is isomorphic to an algebra of vertical cohomologies of the foliation corresponding to the Poisson structure. 相似文献
17.
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
18.
Massimo Ferrarotti Leslie C. Wilson 《Transactions of the American Mathematical Society》1998,350(5):1957-1975
Suppose we have an -jet field on which is a Whitney field on the nonsingular part of . We show that, under certain hypotheses about the relationship between geodesic and euclidean distance on , if the field is flat enough at the singular part , then it is a Whitney field on (the order of flatness required depends on the coefficients in the hypotheses). These hypotheses are satisfied when is subanalytic. In Section II, we show that a function on can be extended to one on if the differential goes to faster than the order of divergence of the principal curvatures of and if the first covariant derivative of is sufficiently flat. For the general case of functions with , we give a similar result for in Section III.
19.
Reza Sazeedeh 《Proceedings of the American Mathematical Society》2007,135(8):2339-2345
Let be a Noetherian homogeneous ring with local base ring and let be a finitely generated graded -module. Let be the largest integer such that is not Artinian. We will prove that are Artinian for all and there exists a polynomial of degree less than such that for all . Let be the first integer such that the local cohomology module is not cofinite. We will show that for all the graded module is Artinian.
20.
Reza Sazeedeh 《Proceedings Mathematical Sciences》2007,117(4):429-441
Let M be a finitely generated graded module over a Noetherian homogeneous ring R with local base ring (R
0, m0). If R
0 is of dimension one, then we show that reg
i+1(M) and coreg
i+1(M) are bounded for all i ∈ ℕ0. We improve these bounds, if in addition, R
0 is either regular or analytically irreducible of unequal characteristic. 相似文献