Birational geometry | Complex surfaces | Algebraic surfaces

Rational surface

In algebraic geometry, a branch of mathematics, a rational surface is a surface birationally equivalent to the projective plane, or in other words a rational variety of dimension two. Rational surfaces are the simplest of the 10 or so classes of surface in the Enriques–Kodaira classification of complex surfaces,and were the first surfaces to be investigated. (Wikipedia).

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Simplify a rational expression

Learn how to simplify rational expressions. A rational expression is an expression in the form of a fraction where the numerator and/or the denominator are/is an algebraic expression. To simplify a rational expression, we factor completely the numerator and the denominator of the rational

From playlist Simplify Rational Expressions

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Simplifying a rational expression with a trinomial

Learn how to simplify rational expressions. A rational expression is an expression in the form of a fraction where the numerator and/or the denominator are/is an algebraic expression. To simplify a rational expression, we factor completely the numerator and the denominator of the rational

From playlist Simplify Rational Expressions

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Factoring out the GCF to simplify the rational expression

Learn how to simplify rational expressions. A rational expression is an expression in the form of a fraction where the numerator and/or the denominator are/is an algebraic expression. To simplify a rational expression, we factor completely the numerator and the denominator of the rational

From playlist Simplify Rational Expressions (Binomials) #Rational

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Simplify a rational expression

Learn how to simplify rational expressions. A rational expression is an expression in the form of a fraction where the numerator and/or the denominator are/is an algebraic expression. To simplify a rational expression, we factor completely the numerator and the denominator of the rational

From playlist Simplify Rational Expressions

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Simplify a rational expression by factoring

Learn how to simplify rational expressions. A rational expression is an expression in the form of a fraction where the numerator and/or the denominator are/is an algebraic expression. To simplify a rational expression, we factor completely the numerator and the denominator of the rational

From playlist Simplify Rational Expressions

Video thumbnail

Simplify a rational expression

Learn how to simplify rational expressions. A rational expression is an expression in the form of a fraction where the numerator and/or the denominator are/is an algebraic expression. To simplify a rational expression, we factor completely the numerator and the denominator of the rational

From playlist Simplify Rational Expressions

Video thumbnail

Simplifying rational expression

Learn how to simplify rational expressions. A rational expression is an expression in the form of a fraction where the numerator and/or the denominator are/is an algebraic expression. To simplify a rational expression, we factor completely the numerator and the denominator of the rational

From playlist Simplify Rational Expressions (Binomials) #Rational

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Learning to simplify a rational expression

Learn how to simplify rational expressions. A rational expression is an expression in the form of a fraction where the numerator and/or the denominator are/is an algebraic expression. To simplify a rational expression, we factor completely the numerator and the denominator of the rational

From playlist Simplify Rational Expressions

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What do I need to know to simplify rational expressions

Learn about simplifying rational expressions. A rational expression is an expression in the form of a fraction. To simplify a rational expression is to put the expression in a simplified form i.e. cancel out common factors, etc. When given a rational function such that the numerator and

From playlist Simplify Rational Expressions

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Marcello Bernardara: Semiorthogonal decompositions and birational geometry of geometrically rational

Abstract:This is a joint work in progress with A. Auel. Let S be a geometrically rational del Pezzo surface over a field k. In this talk, I will show how the k-rationality of S is equivalent to the existence of some semiorthogonal decompositions of its derived category. In particular, the

From playlist HIM Lectures: Junior Trimester Program "Algebraic Geometry"

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Rational curves on elliptic surfaces - Douglas Ulmer

A Joint IAS/Princeton University Number Theory Seminar Topic: Rational curves on elliptic surfaces Speaker: Douglas Ulmer Affiliation: Georgia Institute of Technology Date: Thursday, May 5 Given a non-isotrivial elliptic curve EE over K=đť”˝qt K=Fqt, there is always a finite extension L

From playlist Mathematics

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Nick Addington - Rational points and derived equivalence - WAGON

For smooth projective varieties over Q, is the existence of a rational point preserved under derived equivalence? First I'll discuss why this question is interesting, and what is known. Then I'll show that the answer is no, giving two counterexamples: an abelian variety and a torsor over i

From playlist WAGON

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algebraic geometry 33 Rationality of cubic surfaces

This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It gives two rather informal and incomplete arguments for why nonsingular cubic surfaces are rational.

From playlist Algebraic geometry I: Varieties

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Olivier Wittenberg: Sur la conjecture de Hodge entière pour les solides réels

Résumé : Nous formulons un analogue de la conjecture de Hodge entière pour les variétés réelles. Celui-ci possède des liens étroits avec des propriétés classiques: existence d'une courbe réelle de genre pair, algébricité de l'homologie du lieu réel. Comme dans le cas complexe, la conjectur

From playlist Algebraic and Complex Geometry

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Yuri Tschinkel - On the arithmetic of K3 surfaces

Yuri TSCHINKEL (Courant Institute & Simons Foundation, New York, ­USA)

From playlist Algèbre, Géométrie et Physique : une conférence en l'honneur

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Simplifying a rational expression by factoring

Learn how to simplify rational expressions. A rational expression is an expression in the form of a fraction where the numerator and/or the denominator are/is an algebraic expression. To simplify a rational expression, we factor completely the numerator and the denominator of the rational

From playlist Simplify Rational Expressions

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On the algebraic fundamental group of surfaces of general type by Margarida Lopes

Algebraic Surfaces and Related Topics PROGRAM URL : http://www.icts.res.in/program/AS2015 DESCRIPTION : This is a joint program of ICTS with TIFR, Mumbai and KIAS, Seoul. The theory of surfaces has been the cradle to many powerful ideas in Algebraic Geometry. The problems in this area

From playlist Algebraic Surfaces and Related Topics

Related pages

Segre surface | Birational geometry | Enneper surface | Zariski surface | Federigo Enriques | Enriques–Kodaira classification | Unimodular lattice | Bordiga surface | Coble surface | Del Pezzo surface | Cubic surface | Châtelet surface | Fermat cubic | Homological mirror symmetry | Hirzebruch surface | Cayley's nodal cubic surface | Rational variety | Guido Castelnuovo | Mathematics | Veronese surface | White surface | Algebraic geometry | Picard group | Blowing up | Fundamental group | Projective plane | Enriques surface