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ALGEBRAIC GEOMETRY
"... Algebraic geometry is the mathematical study of geometric objects by means of algebra. Its origins go back to the coordinate geometry introduced by Descartes. A classic example is the circle of radius 1 in the plane, which is ..."
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Cited by 513 (6 self)
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Algebraic geometry is the mathematical study of geometric objects by means of algebra. Its origins go back to the coordinate geometry introduced by Descartes. A classic example is the circle of radius 1 in the plane, which is
Algebraic Geometry
, 2002
"... Notes for a class taught at the University of Kaiserslautern 2002/2003 ..."
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Cited by 51 (0 self)
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Notes for a class taught at the University of Kaiserslautern 2002/2003
Improved Decoding of ReedSolomon and AlgebraicGeometry Codes
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 1999
"... Given an errorcorrecting code over strings of length n and an arbitrary input string also of length n, the list decoding problem is that of finding all codewords within a specified Hamming distance from the input string. We present an improved list decoding algorithm for decoding ReedSolomon codes ..."
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Cited by 345 (44 self)
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Given an errorcorrecting code over strings of length n and an arbitrary input string also of length n, the list decoding problem is that of finding all codewords within a specified Hamming distance from the input string. We present an improved list decoding algorithm for decoding ReedSolomon codes. The list decoding problem for ReedSolomon codes reduces to the following "curvefitting" problem over a field F : Given n points f(x i :y i )g i=1 , x i
PRIMER FOR THE ALGEBRAIC GEOMETRY OF SANDPILES
"... Abstract. This is a draft of a primer on the algebraic geometry of the Abelian ..."
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Cited by 8 (1 self)
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Abstract. This is a draft of a primer on the algebraic geometry of the Abelian
Algebras with the same (algebraic) geometry
, 2009
"... Some basic notions of classical algebraic geometry can be defined in arbitrary varieties of algebras Θ. For every algebra H in Θ one can consider algebraic geometry in Θ over H. Correspondingly, algebras in Θ are considered with the emphasis on equations and geometry. We give examples of geometric ..."
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Cited by 31 (11 self)
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Some basic notions of classical algebraic geometry can be defined in arbitrary varieties of algebras Θ. For every algebra H in Θ one can consider algebraic geometry in Θ over H. Correspondingly, algebras in Θ are considered with the emphasis on equations and geometry. We give examples
Algebraic Geometry
"... Version 5.20 September 14, 2009These notes are an introduction to the theory of algebraic varieties. In contrast to most such accounts they study abstract algebraic varieties, and not just subvarieties of affine and projective space. This approach leads more naturally into scheme theory. BibTeX info ..."
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Cited by 2 (0 self)
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Version 5.20 September 14, 2009These notes are an introduction to the theory of algebraic varieties. In contrast to most such accounts they study abstract algebraic varieties, and not just subvarieties of affine and projective space. This approach leads more naturally into scheme theory. Bib
Algebraic Geometry
"... pour i = 1,..., n + k + 2 et S ' En+k−1(Cn), ou ̀ En+k−1(Cn) est le fibre ́ de Schwarzenberger sur Pn appartenant a ̀ Sn,k associe ́ a ̀ la courbe Cn ⊂ P∨n. On en déduit qu’un fibre ́ de Steiner S ∈ Sn,k, s’il n’est pas un fibre ́ de Schwarzenberger, possède au plus (n+ k+1) hyperplans instab ..."
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pour i = 1,..., n + k + 2 et S ' En+k−1(Cn), ou ̀ En+k−1(Cn) est le fibre ́ de Schwarzenberger sur Pn appartenant a ̀ Sn,k associe ́ a ̀ la courbe Cn ⊂ P∨n. On en déduit qu’un fibre ́ de Steiner S ∈ Sn,k, s’il n’est pas un fibre ́ de Schwarzenberger, possède au plus (n+ k+1) hyperplans instables; ceci prouve dans tous les cas un résultat de Dolgachev et Kapranov ([DK], thm. 7.2) concernant les fibrés logarithmiques. ABSTRACT — Let Sn,k denote the family of Steiner’s bundle S on Pn defined by the exact sequence (k> 0) 0 → kOPn(−1) − → (n+ k)OPn − → S → 0 We show the following result: Let S ∈ Sn,k and H1, · · ·,Hn+k+2 distincts hyperplanes such that h0(S∨Hi) 6 = 0. Then it exists a rational normal curve Cn ⊂ P∨n such that Hi ∈ Cn for i = 1,..., n + k + 2 and S ' En+k−1(Cn), where En+k−1(Cn) is the Schwarzenberger’s bundle on Pn which belongs to Sn,k associated to Cn ⊂ P∨n It implies that a Steiner’s bundle S ∈ Sn,k, if it isn’t a Schwarzenberger’s bundle, possesses no more than (n + k + 1) unstable hyperplanes; this proves in any case a result of Dolgachev and Kapranov ([DK], thm 7.2) about logarithmic bundles. 1
Algebraic Geometry
"... 1.1 The Riemann zeta function.................................. 9 1.2 Rings of finite type...................................... 9 ..."
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1.1 The Riemann zeta function.................................. 9 1.2 Rings of finite type...................................... 9
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