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180,203
The Algebraic Curve of
, 2005
"... We investigate the monodromy of the Lax connection for classical IIB superstrings on AdS5 ×S 5. For any solution of the equations of motion we derive a spectral curve of degree 4 +4. The curve consists purely of conserved quantities, all gauge degrees of freedom have been eliminated in this form. Th ..."
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. The most relevant quantities of the solution, such as its energy, can be expressed through certain holomorphic integrals on the curve. This allows for a classification of finite gap solutions analogous to the general solution of strings in flat space. The role of fermions in the context of the algebraic
Vertex algebras and algebraic curves
 Mathematical Surveys and Monographs 88 (2001), Amer. Math.Soc. MR1849359 (2003f:17036
"... Vertex operators appeared in the early days of string theory as local operators describing propagation of string states. Mathematical analogues of these operators were discovered in representation theory of affine KacMoody algebras in the works of Lepowsky–Wilson [LW] and I. Frenkel–Kac [FK]. In or ..."
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Cited by 177 (10 self)
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Vertex operators appeared in the early days of string theory as local operators describing propagation of string states. Mathematical analogues of these operators were discovered in representation theory of affine KacMoody algebras in the works of Lepowsky–Wilson [LW] and I. Frenkel–Kac [FK
AND ALGEBRAIC CURVES BY
"... The explicit linearization of the Korteweg—de Vries equation [10, 18] and the Toda lattice equations [10, 12, 22] led to a theory relating periodic second order (differential and difference) operators to hyperelliptic curves with branch points given by the periodic and antiperiodic spectrum of the o ..."
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with certain properties lead to commuting differential operators reconfirming forgotten work by Burchnell and Chaundy [6]. Inspired by Krichever's ideas, Mumford [24] establishes then a dictionary between commutative rings of (differential and difference) operators and algebraic curves using purely
PARAMETRIZATIONS OF ALGEBRAIC CURVES
"... Abstract. We show that if a pair of meromorphic functions parametrize an algebraic curve then they have a common right factor, and we use this to derive a variety of results on algebraic curves. 1. ..."
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Abstract. We show that if a pair of meromorphic functions parametrize an algebraic curve then they have a common right factor, and we use this to derive a variety of results on algebraic curves. 1.
Authentication Codes and Algebraic Curves
"... Abstract. We survey a recent application of algebraic curves over finite fields to the constructions of authentication codes. 1. ..."
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Cited by 1 (0 self)
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Abstract. We survey a recent application of algebraic curves over finite fields to the constructions of authentication codes. 1.
COMPUTATIONAL ALGEBRA AND ALGEBRAIC CURVES
, 2006
"... Abstract. The development of computational techniques in the last decade has made possible to attack some classical problems of algebraic geometry. In this survey, we briefly describe some open problems related to algebraic curves which can be approached from a computational viewpoint. 1. ..."
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Cited by 4 (4 self)
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Abstract. The development of computational techniques in the last decade has made possible to attack some classical problems of algebraic geometry. In this survey, we briefly describe some open problems related to algebraic curves which can be approached from a computational viewpoint. 1.
The join of algebraic curves
, 2000
"... Abstract. An effective description of the join of algebraic curves in the complex projective space P n is given. 1 ..."
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Abstract. An effective description of the join of algebraic curves in the complex projective space P n is given. 1
Fairness criteria for algebraic curves
 COMPUTING
, 2003
"... We develop methods for the variational design of algebraic curves. Our approach is based on truly geometric fairness criteria, such as the elastic bending energy. In addition, we take certain feasibility criteria for the algebraic curve segment into account. We describe a computational technique for ..."
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Cited by 1 (0 self)
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We develop methods for the variational design of algebraic curves. Our approach is based on truly geometric fairness criteria, such as the elastic bending energy. In addition, we take certain feasibility criteria for the algebraic curve segment into account. We describe a computational technique
ALGEBRAIC CURVES AND CRYPTOGRAPHY
"... Abstract. Algebraic curves over finite fields are being extensively used in the design of publickey cryptographic schemes. This paper surveys some topics in algebraic curve cryptography, with an emphasis on recent developments in algorithms for the elliptic and hyperelliptic curve discrete logarith ..."
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Cited by 5 (0 self)
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Abstract. Algebraic curves over finite fields are being extensively used in the design of publickey cryptographic schemes. This paper surveys some topics in algebraic curve cryptography, with an emphasis on recent developments in algorithms for the elliptic and hyperelliptic curve discrete
Cherednik algebras for algebraic curves
"... Abstract. For any algebraic curve C and n ≥ 1, P. Etingof introduced a ‘global ’ Cherednik algebra as a natural deformation of the cross product D(C n)⋊Sn, of the algebra of differential operators on C n and the symmetric group. We provide a construction of the global Cherednik algebra in terms of q ..."
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Cited by 5 (1 self)
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Abstract. For any algebraic curve C and n ≥ 1, P. Etingof introduced a ‘global ’ Cherednik algebra as a natural deformation of the cross product D(C n)⋊Sn, of the algebra of differential operators on C n and the symmetric group. We provide a construction of the global Cherednik algebra in terms
Results 1  10
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180,203