By F. L. Zak
Over the last 20 years algebraic geometry has skilled a extraordinary shift from improvement of summary theories to research of concrete houses of projective types. Many difficulties of classical algebraic geometry based on linear platforms, projections, embedded tangent areas, etc. Use of contemporary ideas has made it attainable to make growth on a few of these difficulties. Following those topics, this publication covers those subject matters, between others: tangent areas to subvarieties of projective areas and complicated tori, projections of algebraic forms, category of Severi forms, greater secant types, and type of Scorza types over an algebraically closed box of attribute 0.
Read or Download Tangents and Secants of Algebraic Varieties PDF
Best algebra & trigonometry books
College algebra : concepts & contexts
This article bridges the space among conventional and reform techniques to algebra encouraging scholars to determine arithmetic in context. It offers fewer issues in better intensity, prioritizing facts research as a starting place for mathematical modeling, and emphasizing the verbal, numerical, graphical and symbolic representations of mathematical recommendations in addition to connecting arithmetic to genuine existence occasions drawn from the scholars' majors.
Vertiefung Mathematik Primarstufe — Arithmetik/Zahlentheorie
Aufbauend auf ihrem Band „Einführung Mathematik Primarstufe – Arithmetik“ vertiefen die Autoren elementares mathematisches Hintergrundwissen zur Arithmetik/Zahlentheorie vor allem für Lehramtsstudierende der Primarstufe. Themen des Buches sind spannende zahlentheoretische Problemstellungen als Einstieg, Teiler/Vielfache/Reste, Primzahlen unter vielen faszinierenden Aspekten und speziell als Bausteine der natürlichen Zahlen, größter gemeinsamer Teiler und kleinstes gemeinsames Vielfaches, Teilbarkeitsregeln im Dezimalsystem und in anderen Stellenwertsystemen, Dezimalbrüche, Restklassen/algebraische Strukturen sowie praktische Anwendungen (Prüfziffernverfahren und ihre Sicherheit).
General Orthogonal Polynomials
During this treatise, the authors current the overall conception of orthogonal polynomials at the complicated aircraft and several other of its purposes. The assumptions at the degree of orthogonality are basic, the one limit is that it has compact aid at the advanced aircraft. within the improvement of the speculation the most emphasis is on asymptotic habit and the distribution of zeros.
- Set theory and logic
- Matrix Polynomials
- Lecture Notes on Cluster Algebras
- Puzzles and Paradoxes
- Motives (Proceedings of Symposia in Pure Mathematics) (Part 2)
Additional resources for Tangents and Secants of Algebraic Varieties
Sample text
Summing up, we obtain the following result. 8. Theorem. If a variety X n ⊂ PN corresponds to the orbit of highest weight vector of an irreducible representation of a simple Lie group G and dim SX < N ≤ 2n + 1, then X is one of the seven varieties A1 )–A4 ), C), E), F). The varieties A1 ), A3 ), and E) are Severi varieties, and the varieties A0 ), A2 ), C), and F) are hyperplane sections of Severi varieties. 8 we obtain the following result. 9. Theorem. Over an algebraically closed field K of characteristic zero there exist exactly four Severi varieties corresponding to orbits of linear actions of algebraic groups, viz.
E. codimPN X n = N − n ≥ 2N ≥ 2s + 2 ≥ 2n + r − b + 2, 1 (r − b) + 1. 2 42 II. 2. Corollary. Let Y r ⊂ X n ⊂ PN , where X is nonsingular in a neighborhood of Y . Suppose that there is a point u ∈ PN \ X such that the projection π : X → PN −1 with center at u is a closed embedding in a neighborhood of Y . Then N ≥ n + 12 (r + 3). 3. Remark. 1 (resp. 2) is true if instead of assuming that π is a J-embedding with respect to Y (resp. an embedding in a neighborhood of Y ) we assume that π is J-unramified with respect to Y (resp.
Gv and 0, and therefore all Λi are collinear (cf. [17], [85]). On the other hand, since Gv is a cone, all Λi lie in an affine hyperplane (cf. [17]). Thus we may assume that r = 1 and Gv is the orbit of highest weight vector of an irreducible representation of a semisimple group G (varieties of such type were considered in [95] and were called HV -varieties). In particular, from this it follows that the variety X = Gv/K ∗ ⊂ PN is rational (cf. 3 below) and is defined in PN by quadratic equations (cf.