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Titlebook: Discriminants, Resultants, and Multidimensional Determinants; Israel M. Gelfand,Mikhail M. Kapranov,Andrei V. Ze Book 1994 Springer Scienc

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书目名称Discriminants, Resultants, and Multidimensional Determinants
编辑Israel M. Gelfand,Mikhail M. Kapranov,Andrei V. Ze
视频video
概述The definitive text on eliminator theory.Revives the classical theory of resultants and discriminants.Presents both old and new results of the theory
丛书名称Modern Birkhäuser Classics
图书封面Titlebook: Discriminants, Resultants, and Multidimensional Determinants; Israel M. Gelfand,Mikhail M. Kapranov,Andrei V. Ze Book 1994 Springer Scienc
描述.“This book revives and vastly expands the classical theory of resultants and discriminants. Most of the main new results of the book have been published earlier in more than a dozen joint papers of the authors. The book nicely complements these original papers with many examples illustrating both old and new results of the theory.”..Mathematical Reviews..“Collecting and extending the fundamental and highly original results of the authors, it presents a unique blend of classical mathematics and very recent developments in algebraic geometry, homological algebra, and combinatorial theory.”..Zentralblatt Math.  .             .
出版日期Book 1994
关键词algebra; algebraic geometry; elimination theory; geometry; hyperdeterminants; mathematics; polytopes; resul
版次1
doihttps://doi.org/10.1007/978-0-8176-4771-1
isbn_softcover978-0-8176-4770-4
isbn_ebook978-0-8176-4771-1Series ISSN 2197-1803 Series E-ISSN 2197-1811
issn_series 2197-1803
copyrightSpringer Science+Business Media New York 1994
The information of publication is updating

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Toric Varietiesoses. Since there are several references available on the subject [D] [Fu 2] [O], we did not attempt to be exhaustive or self-contained. Our exposition is organized “from the special to the general” so that the general description of toric varieties in terms of fans appears at the very end of the chapter.
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Regular A-Determinants and A-Discriminantsg the polynomials Δ. and .. that allows us to recover Δ. as as an alternating product of the ... Consequently, alternating sums and products will appear in the expressions for the Newton polytope and coefficients of Δ..
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Discriminants and Resultants for Forms in Several Variablesvery special cases. The methods developed in Parts I and II help to put this and other questions in a general perspective. Without pretending to be complete, we present an overview of some fairly classical results together with more fresh developments.
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The Cayley Method for Studying Discriminantsl Δ.. The method goes back to the remarkable paper by Cayley [Ca4] on elimination theory, in which the foundations were laid for what is now called homological algebra. The Cayley method can also be applied to other similar problems, such as finding resultants (see Chapter 3).
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