This article grew out of a sophisticated direction taught via the writer on the Fourier Institute (Grenoble, France). It serves as an advent to the combinatorics of symmetric services, extra accurately to Schur and Schubert polynomials. additionally studied is the geometry of Grassmannians, flag types, and particularly, their Schubert kinds. This publication examines profound connections that unite those matters. The publication is split into 3 chapters. the 1st is dedicated to symmetric features and particularly to Schur polynomials. those are polynomials with optimistic integer coefficients during which all of the monomials correspond to a tender tableau with the valuables of being 'semistandard'. the second one bankruptcy is dedicated to Schubert polynomials, which have been came across through A. Lascoux and M. P. Schutzenberger who deeply probed their combinatorial properties.It is proven, for instance, that those polynomials help the sophisticated connections among difficulties of enumeration of decreased decompositions of variations and the Littlewood-Richardson rule, a very efficacious model of that could be derived from those connections. the ultimate bankruptcy is geometric. it's dedicated to Schubert types, subvarieties of Grassmannians, and flag types outlined by means of yes occurrence stipulations with fastened subspaces. This quantity makes obtainable a couple of effects, making a strong stepping stone for scaling extra bold heights within the quarter. The author's reason used to be to stay hassle-free: the 1st chapters require no past wisdom, the 3rd bankruptcy makes use of a few rudimentary notions of topology and algebraic geometry. for that reason, a complete appendix at the topology of algebraic forms is supplied. This ebook is the English translation of a textual content formerly released in French.
Read Online or Download Symmetric Functions, Schubert Polynomials and Degeneracy Loci (Smf/Ams Texts and Monographs, Vol 6 and Cours Specialises Numero 3, 1998) PDF
Similar Algebraic Geometry books
This paintings attracts jointly rules from algebraic topology, practical research and geometry. it's a software - a way of conveying info between those 3 topics - and it's been used with luck to find theorems throughout a large span of arithmetic. the aim of this ebook is to acquaint the reader with the fundamental principles of analytic K-homology and strengthen a few of its purposes.
In providing a close research of the geometry and topology of various periods of "generic" singularities, Geometry of Topological balance bridges the space among algebraic calculations and continuity arguments to element the mandatory and enough stipulations for a C (infinity) to be C]0-stable. all through, the authors masterfully study this significant topic utilizing effects culled from a vast diversity of mathematical disciplines, together with geometric topology, stratification idea, algebraic geometry, and commutative algebra.
According to a graduate path on the Technische Universität, Berlin, those lectures current a wealth of fabric at the glossy idea of convex polytopes. the simple exposition positive aspects many illustrations, and whole proofs for many theorems. With merely linear algebra as a prerequisite, it takes the reader quick from the fundamentals to subject matters of modern examine.
The class conception of algebraic forms is the focal point of this booklet. This very lively sector of analysis continues to be constructing, yet an grand volume of data has collected during the last 20 years. The authors aim is to supply an simply available advent to the topic. The publication begins with preparatory and conventional definitions and effects, then strikes directly to talk about a variety of facets of the geometry of gentle projective kinds with many rational curves, and finishes in taking the 1st steps in the direction of Moris minimum version software of class of algebraic forms via proving the cone and contraction theorems.
Extra info for Symmetric Functions, Schubert Polynomials and Degeneracy Loci (Smf/Ams Texts and Monographs, Vol 6 and Cours Specialises Numero 3, 1998)