On the classification of real mono-germs of corank one and codimension one
Kevin Houston (2004)
Banach Center Publications
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Corank one mono-germs , n < p, of -codimension one are classified by giving an explicit normal form.
Kevin Houston (2004)
Banach Center Publications
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Corank one mono-germs , n < p, of -codimension one are classified by giving an explicit normal form.
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 defined on , . This lower bound is related to the sum of the absolute values of the indices of at and .
Joseph Cima, Raymond Mortini (1995)
Studia Mathematica
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It is shown that the Bourgain algebra of the disk algebra A() with respect to is the algebra generated by the Blaschke products having only a finite number of singularities. It is also proved that, with respect to , the algebra QA of bounded analytic functions of vanishing mean oscillation is invariant under the Bourgain map as is .
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 with in a Lie algebra of type or (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.
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 -spin theory of Jarvis-Kimura-Vaintrob. We further prove that for a singularity of type our construction of the stack of -curves is canonically isomorphic to the stack of -spin curves described by Abramovich and Jarvis. We further prove that our theory satisfies all the Jarvis-Kimura-Vaintrob axioms for an -spin virtual class. Therefore, the Faber-Shadrin-Zvonkine...
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 , fixed point of the vector fields. We define a “Diophantine condition” on the quasihomogeneous initial part which ensures that if such a perturbation of is formally conjugate to then it is also holomorphically conjugate to it. We study the normal form problem relatively to . We give a condition on that ensures...
Abdelmalek Azizi, Mohamed Mahmoud Chems-Eddin, Abdelkader Zekhnini (2021)
Commentationes Mathematicae Universitatis Carolinae
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Let be a square free integer and . In the present work we determine all the fields such that the -class group, , of is of type or .
J. H. Rieger, M. A. S. Ruas, R. Wik Atique (2008)
Banach Center Publications
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A stable deformation of a real map-germ is said to be an M-deformation if all isolated stable (local and multi-local) singularities of its complexification are real. A related notion is that of a good real perturbation 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 coincides with that of . The class of map germs having an M-deformation is, in some sense, much larger than the one having a good...
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 for two rational functions , in term of the degree of , which is sharp whenever have few distinct zeros and poles compared to their degree. This sharpens the “-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 contains only finitely many rational or elliptic...
Céline Roucairol (2006)
Bulletin de la Société Mathématique de France
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In -modules theory, Gauss-Manin systems are defined by the direct image of the structure sheaf 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 of a -module twisted by the exponential of a polynomial by another polynomial , where and are two polynomials in two variables. The analogue of the Gauss-Manin systems can...
W. M. Mikulski (2002)
Colloquium Mathematicae
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Let r and n be natural numbers. For n ≥ 2 all natural operators transforming vector fields on n-manifolds M to 1-forms on are classified. For n ≥ 3 all natural operators transforming vector fields on n-manifolds M to 2-forms on are completely described.
Daniel C. Mayer (2014)
Journal de Théorie des Nombres de Bordeaux
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For an algebraic number field with -class group of type , the structure of the -class groups of the four unramified cyclic cubic extension fields , , of is calculated with the aid of presentations for the metabelian Galois group of the second Hilbert -class field of . In the case of a quadratic base field it is shown that the structure of the -class groups of the four -fields frequently determines the type of principalization of the -class group of in . This...
Mark van Hoeij, Vivek Pal (2012)
Journal de Théorie des Nombres de Bordeaux
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Let and be algebraic number fields. We describe a new method to find (if they exist) all isomorphisms, . The algorithm is particularly efficient if there is only one isomorphism.
Jia Chao (1974)
Studia Mathematica
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Srinivas Kotyada, Subramani Muthukrishnan (2018)
Czechoslovak Mathematical Journal
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Let be an algebraic number field of class number one and let be its ring of integers. We show that there are infinitely many non-Wieferich primes with respect to certain units in under the assumption of the -conjecture for number fields.
Mohamed Mahmoud Chems-Eddin, Abdelmalek Azizi, Abdelkader Zekhnini (2021)
Archivum Mathematicum
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Let be an odd square-free integer, any integer and . In this paper, we shall determine all the fields having an odd class number. Furthermore, using the cyclotomic -extensions of some number fields, we compute the rank of the -class group of whenever the prime divisors of are congruent to or .
Jacek Dębecki (2016)
Czechoslovak Mathematical Journal
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We give a classification of all linear natural operators transforming -vectors (i.e., skew-symmetric tensor fields of type ) on -dimensional manifolds to tensor fields of type on , where is a Weil bundle, under the condition that , and . The main result of the paper states that, roughly speaking, each linear natural operator lifting -vectors to tensor fields of type on is a sum of operators obtained by permuting the indices of the tensor products of linear natural...