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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
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TL;DR: A generalization of Newton’s method to deal with solution paths defined by polynomial homotopies that lead to extremal values is defined andEmbedding the solutions in a toric variety leads to explicit scaling relations between coefficients and solutions.
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Delay-margin design for the general class of single-delay retarded-type LTI systems
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The tropical $j$-invariant
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Permanent versus determinant: not via saturations
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A Novel Frequency-Domain Approach for the Exact Range of Imaginary Spectra and the Stability Analysis of LTI Systems With Two Delays
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References
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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.
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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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