A discrete phenomenon in propagation of singularities
Paul Godin (1987)
Banach Center Publications
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Paul Godin (1987)
Banach Center Publications
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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.
Bronisław Jakubczyk, Feliks Przytycki
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CONTENTSIntroduction............................................................................51. The main ideas and results................................................62. -invariant subsets of .........................223. Reduction to germs of differential 1-forms........................354. The case k ≥ 2n-3. Proof of Theorem A...........................445. The case n = 3, k = 2.......................................................46Appendix. Connections with control theory...........................59List...
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.
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 .
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...
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...
Wided Chikouche, Serge Nicaise (2008)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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We study the regularity of the solution of the regularized electric Maxwell problem in a polygonal domain with data in . Using a duality method, we prove a decomposition of the solution into a regular part in the non-Hilbertian Sobolev space and an explicit singular one.
Janusz Gwoździewicz, Arkadiusz Płoski (2005)
Colloquium Mathematicae
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For every polynomial F in two complex variables we define the Łojasiewicz exponents measuring the growth of the gradient ∇F on the branches centered at points p at infinity such that F approaches t along γ. We calculate the exponents in terms of the local invariants of singularities of the pencil of projective curves associated with F.
M. Corrêa Jr, A. Fernández-Pérez, G. Nonato Costa, R. Vidal Martins (2014)
Annales de l’institut Fourier
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Let be a holomorphic one-dimensional foliation on such that the components of its singular locus are curves and points . We determine the number of , counted with multiplicities, in terms of invariants of and , assuming that is special along the . Allowing just one nonzero dimensional component on , we also prove results on when the foliation happens to be determined by its singular locus.
J. Feldman (1986)
Recherche Coopérative sur Programme n°25
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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...
Gavril Farkas, Katharina Ludwig (2010)
Journal of the European Mathematical Society
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We study the enumerative geometry of the moduli space of Prym varieties of dimension . Our main result is that the compactication of is of general type as soon as and is different from 15. We achieve this by computing the class of two types of cycles on : one defined in terms of Koszul cohomology of Prym curves, the other defined in terms of Raynaud theta divisors associated to certain vector bundles on curves. We formulate a Prym–Green conjecture on syzygies of Prym-canonical...
Z. Ditzian, S. Tikhonov (2007)
Studia Mathematica
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Relations between moduli of smoothness of the derivatives of a function and those of the function itself are investigated. The results are for and for 0 < p < ∞ using the moduli of smoothness and respectively.
Henri Guenancia (2014)
Annales de l’institut Fourier
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Let be a compact Kähler manifold and be a -divisor with simple normal crossing support and coefficients between and . Assuming that is ample, we prove the existence and uniqueness of a negatively curved Kahler-Einstein metric on having mixed Poincaré and cone singularities according to the coefficients of . As an application we prove a vanishing theorem for certain holomorphic tensor fields attached to the pair .
Michał Kowalczyk, Yong Liu, Frank Pacard (2013-2014)
Séminaire Laurent Schwartz — EDP et applications
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An entire solution of the Allen-Cahn equation , where is an odd function and has exactly three zeros at and , e.g. , is called a end solution if its nodal set is asymptotic to half lines, and if along each of these half lines the function looks (up to a multiplication by ) like the one dimensional, odd, heteroclinic solution , of . In this paper we present some recent advances in the theory of the multiple end solutions. We begin with the description of the moduli space...
Xinhong Chen, Ming Lu (2015)
Colloquium Mathematicae
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Let K be an algebraically closed field. Let (Q,Sp,I) be a skewed-gentle triple, and let and be the corresponding skewed-gentle pair and the associated gentle pair, respectively. We prove that the skewed-gentle algebra is singularity equivalent to KQ/⟨I⟩. Moreover, we use (Q,Sp,I) to describe the singularity category of . As a corollary, we find that if and only if if and only if .
Claire Voisin (2013)
Annales scientifiques de l'École Normale Supérieure
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We prove that Bloch’s conjecture is true for surfaces with obtained as -sets of a section of a very ample vector bundle on a variety with “trivial” Chow groups. We get a similar result in presence of a finite group action, showing that if a projector of the group acts as on holomorphic -forms of , then it acts as on -cycles of degree of . In higher dimension, we also prove a similar but conditional result showing that the generalized Hodge conjecture for general ...
Özer Öztürk (2010)
Annales Polonici Mathematici
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We give a closed formula for the Thom polynomials of the singularities in terms of Schur functions. Our computations combine the characterization of the Thom polynomials via the “method of restriction equations” of Rimányi et al. with the techniques of Schur functions.
Tommaso de Fernex, Mircea Mustață (2009)
Annales scientifiques de l'École Normale Supérieure
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Let denote the set of log canonical thresholds of pairs , with a nonsingular variety of dimension , and a nonempty closed subscheme of . Using non-standard methods, we show that every limit of a decreasing sequence in lies in , proving in this setting a conjecture of Kollár. We also show that is closed in ; in particular, every limit of log canonical thresholds on smooth varieties of fixed dimension is a rational number. As a consequence of this property, we see that in...
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 .
Enrica Floris (2013)
Annales de l’institut Fourier
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In this work we study the moduli part in the canonical bundle formula of an lc-trivial fibration whose general fibre is a rational curve. If is the Cartier index of the fibre, it was expected that would provide a bound on the denominators of the moduli part. Here we prove that such a bound cannot even be polynomial in , we provide a bound and an example where the smallest integer that clears the denominators of the moduli part is . Moreover we prove that even locally the denominators...