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110
Stability of the Poincaré bundle
 Math. Nachr
, 1997
"... Let C be a nonsingular projective curve of genus g ≥ 2 defined over the complex numbers, and let Mξ denote the moduli space of stable bundles of rank n and determinant ξ on C, where ξ is a line bundle of degree d on C and n and d are coprime. It is shown that the universal bundle Uξ on C × Mξ is sta ..."
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Cited by 6 (4 self)
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Let C be a nonsingular projective curve of genus g ≥ 2 defined over the complex numbers, and let Mξ denote the moduli space of stable bundles of rank n and determinant ξ on C, where ξ is a line bundle of degree d on C and n and d are coprime. It is shown that the universal bundle Uξ on C × Mξ
Poincaré, relativity, billiards and symmetry
, 2005
"... This review is made of two parts which are related to Poincaré in different ways. The first part reviews the work of Poincaré on the Theory of (Special) Relativity. One emphasizes both the remarkable achievements of Poincaré, and the fact that he never came close to what is the essential conceptual ..."
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Cited by 1 (0 self)
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This review is made of two parts which are related to Poincaré in different ways. The first part reviews the work of Poincaré on the Theory of (Special) Relativity. One emphasizes both the remarkable achievements of Poincaré, and the fact that he never came close to what is the essential conceptual
Chiral Poincaré duality
, 1999
"... 1. Let X be a smooth algebraic variety over C. In the note [MSV] we introduced a sheaf of vertex superalgebras Ωch X on X. (Below we will often omit the prefix ”super”; we will live mainly in the Z/2graded world, the tilde over a letter will denote its parity.) This sheaf has a Z × Z≥0grading Ω ch ..."
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Cited by 7 (4 self)
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. carries a canonical finite filtration whose factors are locally free OXmodules of finite rank. However, there is no natural OXmodule structure itself. Let us consider the cohomology Each component Ω ch,p i on Ω ch
Rank properties of Poincaré maps for hybrid systems with applications to bipedal walking
 in Hybrid Systems: Computation and Control, pp.151–160
, 2010
"... The equivalence of the stability of periodic orbits with the stability of fixed points of a Poincare ́ map is a wellknown fact for smooth dynamical systems. In particular, the eigenvalues of the linearization of a Poincare ́ map can be used to determine the stability of periodic orbits. The main o ..."
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Cited by 7 (5 self)
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to 0 and the number of trivial eigenvalues is bounded above by dimensionality differences between the different discrete domains of the hybrid system and the rank of the reset maps. Specifically, if n is the minimum dimension of the domains of the hybrid system, then the Poincare ́ map on a domain
POINCARE POLYNOMIALS AND LEVEL RANK DUALITIES IN THE N = 2 COSET CONSTRUCTION
, 1993
"... We review the coset construction of conformal field theories; the emphasis is on the construction of the Hilbert spaces for these models, especially if fixed points occur. This is applied to the N = 2 superconformal cosets constructed by Kazama and Suzuki. To calculate heterotic string spectra we re ..."
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Cited by 1 (1 self)
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reformulate the Gepner construction in terms of simple currents and introduce the socalled extended Poincaré polynomial. We finally comment on the various equivalences arising between models of this class, which can be expressed as level rank dualities.
ON POINCARÉ BUNDLES OF VECTOR BUNDLES ON CURVES
, 2004
"... Abstract. Let M denote the moduli space of stable vector bundles of rank n and fixed determinant of degree coprime to n on a nonsingular projective curve X of genus g ≥ 2. Denote by U a universal bundle on X × M. We show that, for x, y ∈ X, x ̸ = y, the restrictions U{x} × M and U{y} × M are st ..."
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Cited by 4 (1 self)
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Abstract. Let M denote the moduli space of stable vector bundles of rank n and fixed determinant of degree coprime to n on a nonsingular projective curve X of genus g ≥ 2. Denote by U a universal bundle on X × M. We show that, for x, y ∈ X, x ̸ = y, the restrictions U{x} × M and U{y} × M
ON POINCARE POLYNOMIALS OF HYPERBOLIC LIE ALGEBRAS
, 706
"... Poincare polynomials are known only for Finite and also Affine types of KacMoody Lie algebras. It is therefore worthwhile to study the cases beyond Affine KacMoody Lie algebras. To this end, we present a method for calculation of Poincare polynomials. Our method can be applied equally well for any ..."
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for any types of KacMoody Lie algebras. Particular attention is given here for 48 Hyperbolic Lie algebras of ranks N=3,4,5,6. Our method is based on numerical calculations as usual in any calculation of affine string functions. The results show that there is a significant form for hyperbolic Poincare
STABILITY OF PROJECTIVE POINCARÉ AND PICARD BUNDLES
, 2008
"... Let X be an irreducible smooth projective curve of genus g ≥ 3 defined over the complex numbers and let Mξ denote the moduli space of stable vector bundles on X of rank n and determinant ξ, where ξ is a fixed line bundle of degree d. If n and d have a common divisor, there is no universal vector bu ..."
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Cited by 1 (1 self)
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Let X be an irreducible smooth projective curve of genus g ≥ 3 defined over the complex numbers and let Mξ denote the moduli space of stable vector bundles on X of rank n and determinant ξ, where ξ is a fixed line bundle of degree d. If n and d have a common divisor, there is no universal vector
The f(q) mock theta function conjecture and partition ranks
, 2005
"... In 1944, Freeman Dyson initiated the study of ranks of integer partitions. Here we solve the classical problem of obtaining formulas for Ne(n) (resp. No(n)), the number of partitions of n with even (resp. odd) rank. Thanks to Rademacher’s celebrated formula for the partition function, this problem ..."
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Cited by 95 (36 self)
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In 1944, Freeman Dyson initiated the study of ranks of integer partitions. Here we solve the classical problem of obtaining formulas for Ne(n) (resp. No(n)), the number of partitions of n with even (resp. odd) rank. Thanks to Rademacher’s celebrated formula for the partition function, this problem
Some addition to the generalized RiemannHilbert problem
, 2009
"... ABSTRACT. We consider the generalized RiemannHilbert problem for linear differential equations with irregular singularities. If one weakens the conditions by allowing one of the Poincaré ranks to be nonminimal, the problem is known to have a solution. In this article we give a bound for the poss ..."
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ABSTRACT. We consider the generalized RiemannHilbert problem for linear differential equations with irregular singularities. If one weakens the conditions by allowing one of the Poincaré ranks to be nonminimal, the problem is known to have a solution. In this article we give a bound
Results 1  10
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110