Displaying similar documents to “Singularities of k-tuples of vector fields”

Unit vector fields on antipodally punctured spheres: big index, big volume

Fabiano G. B. Brito, Pablo M. Chacón, David L. Johnson (2008)

Bulletin de la Société Mathématique de France

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We establish in this paper a lower bound for the volume of a unit vector field v defined on 𝐒 n { ± x } , n = 2 , 3 . This lower bound is related to the sum of the absolute values of the indices of v at x and - x .

The Bourgain algebra of the disk algebra A(𝔻) and the algebra QA

Joseph Cima, Raymond Mortini (1995)

Studia Mathematica

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It is shown that the Bourgain algebra A ( ) b of the disk algebra A() with respect to H ( ) is the algebra generated by the Blaschke products having only a finite number of singularities. It is also proved that, with respect to H ( ) , the algebra QA of bounded analytic functions of vanishing mean oscillation is invariant under the Bourgain map as is A ( ) b .

Springer fiber components in the two columns case for types A and D are normal

Nicolas Perrin, Evgeny Smirnov (2012)

Bulletin de la Société Mathématique de France

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We study the singularities of the irreducible components of the Springer fiber over a nilpotent element N with N 2 = 0 in a Lie algebra of type A or D (the so-called two columns case). We use Frobenius splitting techniques to prove that these irreducible components are normal, Cohen–Macaulay, and have rational singularities.

Quantum Singularity Theory for A ( r - 1 ) and r -Spin Theory

Huijun Fan, Tyler Jarvis, Yongbin Ruan (2011)

Annales de l’institut Fourier

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We give a review of our construction of a cohomological field theory for quasi-homogeneous singularities and the r -spin theory of Jarvis-Kimura-Vaintrob. We further prove that for a singularity W of type A our construction of the stack of W -curves is canonically isomorphic to the stack of r -spin curves described by Abramovich and Jarvis. We further prove that our theory satisfies all the Jarvis-Kimura-Vaintrob axioms for an r -spin virtual class. Therefore, the Faber-Shadrin-Zvonkine...

Normal forms of analytic perturbations of quasihomogeneous vector fields: Rigidity, invariant analytic sets and exponentially small approximation

Eric Lombardi, Laurent Stolovitch (2010)

Annales scientifiques de l'École Normale Supérieure

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In this article, we study germs of holomorphic vector fields which are “higher order” perturbations of a quasihomogeneous vector field in a neighborhood of the origin of n , fixed point of the vector fields. We define a “Diophantine condition” on the quasihomogeneous initial part S which ensures that if such a perturbation of S is formally conjugate to S then it is also holomorphically conjugate to it. We study the normal form problem relatively to S . We give a condition on S that ensures...

Real deformations and invariants of map-germs

J. H. Rieger, M. A. S. Ruas, R. Wik Atique (2008)

Banach Center Publications

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A stable deformation f t of a real map-germ f : , 0 p , 0 is said to be an M-deformation if all isolated stable (local and multi-local) singularities of its complexification f t are real. A related notion is that of a good real perturbation f t of f (studied e.g. by Mond and his coworkers) for which the homology of the image (for n < p) or discriminant (for n ≥ p) of f t coincides with that of f C t . The class of map germs having an M-deformation is, in some sense, much larger than the one having a good...

An a b c d theorem over function fields and applications

Pietro Corvaja, Umberto Zannier (2011)

Bulletin de la Société Mathématique de France

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We provide a lower bound for the number of distinct zeros of a sum 1 + u + v for two rational functions u , v , in term of the degree of u , v , which is sharp whenever u , v have few distinct zeros and poles compared to their degree. This sharpens the “ a b c d -theorem” of Brownawell-Masser and Voloch in some cases which are sufficient to obtain new finiteness results on diophantine equations over function fields. For instance, we show that the Fermat-type surface x a + y a + z c = 1 contains only finitely many rational or elliptic...

Irregularity of an analogue of the Gauss-Manin systems

Céline Roucairol (2006)

Bulletin de la Société Mathématique de France

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In 𝒟 -modules theory, Gauss-Manin systems are defined by the direct image of the structure sheaf 𝒪 by a morphism. A major theorem says that these systems have only regular singularities. This paper examines the irregularity of an analogue of the Gauss-Manin systems. It consists in the direct image complex f + ( 𝒪 e g ) of a 𝒟 -module twisted by the exponential of a polynomial g by another polynomial  f , where f and g are two polynomials in two variables. The analogue of the Gauss-Manin systems can...

The natural operators T | f T * T r * and T | f Λ ² T * T r *

W. M. Mikulski (2002)

Colloquium Mathematicae

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Let r and n be natural numbers. For n ≥ 2 all natural operators T | f T * T r * transforming vector fields on n-manifolds M to 1-forms on T r * M = J r ( M , ) are classified. For n ≥ 3 all natural operators T | f Λ ² T * T r * transforming vector fields on n-manifolds M to 2-forms on T r * M are completely described.

Principalization algorithm via class group structure

Daniel C. Mayer (2014)

Journal de Théorie des Nombres de Bordeaux

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For an algebraic number field K with 3 -class group Cl 3 ( K ) of type ( 3 , 3 ) , the structure of the 3 -class groups Cl 3 ( N i ) of the four unramified cyclic cubic extension fields N i , 1 i 4 , of K is calculated with the aid of presentations for the metabelian Galois group G 3 2 ( K ) = Gal ( F 3 2 ( K ) | K ) of the second Hilbert 3 -class field F 3 2 ( K ) of K . In the case of a quadratic base field K = ( D ) it is shown that the structure of the 3 -class groups of the four S 3 -fields N 1 , ... , N 4 frequently determines the type of principalization of the 3 -class group of K in N 1 , ... , N 4 . This...

Isomorphisms of algebraic number fields

Mark van Hoeij, Vivek Pal (2012)

Journal de Théorie des Nombres de Bordeaux

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Let ( α ) and ( β ) be algebraic number fields. We describe a new method to find (if they exist) all isomorphisms, ( β ) ( α ) . The algorithm is particularly efficient if there is only one isomorphism.

Non-Wieferich primes in number fields and a b c -conjecture

Srinivas Kotyada, Subramani Muthukrishnan (2018)

Czechoslovak Mathematical Journal

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Let K / be an algebraic number field of class number one and let 𝒪 K be its ring of integers. We show that there are infinitely many non-Wieferich primes with respect to certain units in 𝒪 K under the assumption of the a b c -conjecture for number fields.

On the 2 -class group of some number fields with large degree

Mohamed Mahmoud Chems-Eddin, Abdelmalek Azizi, Abdelkader Zekhnini (2021)

Archivum Mathematicum

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Let d be an odd square-free integer, m 3 any integer and L m , d : = ( ζ 2 m , d ) . In this paper, we shall determine all the fields L m , d having an odd class number. Furthermore, using the cyclotomic 2 -extensions of some number fields, we compute the rank of the 2 -class group of L m , d whenever the prime divisors of d are congruent to 3 or 5 ( mod 8 ) .

Linear natural operators lifting p -vectors to tensors of type ( q , 0 ) on Weil bundles

Jacek Dębecki (2016)

Czechoslovak Mathematical Journal

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We give a classification of all linear natural operators transforming p -vectors (i.e., skew-symmetric tensor fields of type ( p , 0 ) ) on n -dimensional manifolds M to tensor fields of type ( q , 0 ) on T A M , where T A is a Weil bundle, under the condition that p 1 , n p and n q . The main result of the paper states that, roughly speaking, each linear natural operator lifting p -vectors to tensor fields of type ( q , 0 ) on T A is a sum of operators obtained by permuting the indices of the tensor products of linear natural...