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Discriminants, Resultants, and Multidimensional Determinants
Izrailʹ Moiseevich Gelʹfand,Mikhail Kapranov,Andrei Zelevinsky +2 more
- 10 May 2013
3.1K
TL;DR: The Cayley method of studying discriminants was used by Cayley as discussed by the authors to study the Cayley Method of Discriminants and Resultants for Polynomials in One Variable and for forms in Several Variables.
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Abstract: Preface.- Introduction.- General Discriminants and Resultants.- Projective Dual Varieties and General Discriminants.- The Cayley Method of Studying Discriminants.- Associated Varieties and General Resultants.- Chow Varieties.- Toric Varieties.- Newton Polytopes and Chow Polytopes.- Triangulations and Secondary Polytopes.- A-Resultants and Chow Polytopes of Toric Varieties.- A-Discriminants.- Principal A-Discriminants.- Regular A-Determinants and A-Discriminants.- Classical Discriminants and Resultants.- Discriminants and Resultants for Polynomials in One Variable.- Discriminants and Resultants for Forms in Several Variables.- Hyperdeterminants.- Appendix A. Determinants.- Appendix B. A. Cayley: On the Theory of Elimination.- Bibliography.- Notes and References.- List of Notation.- Index
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Citations
Residual resultant over the projective plane and the implicitization problem
Laurent Busé
- 01 Jul 2001
TL;DR: This article generalizes the recent notion of residual resultant of a complete intersection to the case of a local complete intersection of codimension 2 in the projective plane, which is the necessary and sufficient condition for a system of three polynomials to have a solution “outside” a variety.
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Separability problem for multipartite states of rank at most 4
TL;DR: In this paper, it was shown that any PPTP state of rank 2 or 3 is separable and has length at most 4 for some qubit-qutrit or multiqubit states.
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Classification of joint numerical ranges of three hermitian matrices of size three
TL;DR: In this paper, the joint numerical range W (F ) of three hermitian 3-by-3 matrices F = (F 1, F 2, F 3 ) is a convex and compact subset in R 3.
33
Higher-dimensional analogues of stable curves
Valery Alexeev
- 26 Jul 2006
TL;DR: The Minimal Model Program offers natural higher-dimensional analogues of stable n-pointed curves and maps as mentioned in this paper, namely stable pairs consisting of a projective variety X of dimension 2 and a divisor B, that should satisfy a few simple conditions, and stable maps f : (X,B) �¨ Y ��.
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1-efficient triangulations and the index of a cusped hyperbolic 3-manifold
TL;DR: In this paper, the 3D index of an ideal triangulation T of an oriented cusped 3-manifold M (a collection of q-series with integer coefficients, introduced by Dimofte-Gaiotto-Gukov) was promoted to a topological invariant of hyperbolic 3manifolds.
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References
•Book
Real and complex analysis
Walter Rudin
- 01 Jan 1966
TL;DR: In this paper, the Riesz representation theorem is used to describe the regularity properties of Borel measures and their relation to the Radon-Nikodym theorem of continuous functions.
•Book
Basic Algebraic Geometry
Igorʹ Rostislavovich Shafarevich
- 01 Jan 1974
TL;DR: The second volume of Shafarevich's introductory book on algebraic geometry focuses on schemes, complex algebraic varieties and complex manifolds as discussed by the authors, and is suitable for beginning graduate students.
2.1K
•Book
Vector Bundles on Complex Projective Spaces
Christian Okonek,Michael Schneider,Heinz Spindler +2 more
- 01 Jan 1980
1.5K
R-Torsion and the Laplacian on Riemannian manifolds
D.B. Ray,Isadore Manuel Singer +1 more
TL;DR: In this article, it was shown that T = T is a manifold invariant and presented some evidence for T = 7, and that T is independent of the metric of W, for W closed and has even dimension.
1.2K
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