Birational geometry | Algebraic varieties | Field (mathematics)

Rational variety

In mathematics, a rational variety is an algebraic variety, over a given field K, which is birationally equivalent to a projective space of some dimension over K. This means that its function field is isomorphic to the field of all rational functions for some set of indeterminates, where d is the dimension of the variety. (Wikipedia).

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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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Rational Functions

In this video we cover some rational function fundamentals, including asymptotes and interecepts.

From playlist Polynomial Functions

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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 (Binomials) #Rational

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Simplifying a rational expression by factoring two trinomials

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 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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Factoring out the GCF from the denominator to help you simplify your 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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Dividing rational expressions

Learn how to divide rational expressions. A rational expression is an expression in the form of a fraction, usually having variable(s) in the denominator. Recall that to divide by a fraction, we multiply by the reciprocal of the fraction. The same rule applies when we want to divide by a r

From playlist How to Divide Rational Expressions #Rational

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Dividing two rational expressions by factoring

Learn how to divide rational expressions. A rational expression is an expression in the form of a fraction, usually having variable(s) in the denominator. Recall that to divide by a fraction, we multiply by the reciprocal of the fraction. The same rule applies when we want to divide by a r

From playlist How to Divide Rational Expressions #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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Massimiliano Mella: Unirational varieties - Part 1

Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b

From playlist Algebraic and Complex Geometry

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algebraic geometry 31 Rational maps

This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers the definition of rational functions and rational maps, and gives an example of a cubic curve that is not birational to the affine line.

From playlist Algebraic geometry I: Varieties

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Fields Medal Lecture: Classification of algebraic varieties — Caucher Birkar — ICM2018

Classification of algebraic varieties Caucher Birkar Abstract: The aim of this talk is to describe the classification problem of algebraic varieties in the framework of modern birational geometry. This problem which lies at the heart of algebraic geometry has seen tremendous advances in t

From playlist Special / Prizes Lectures

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Benedict Gross: Rational points on hyperelliptic curves [2016]

Rational points on hyperelliptic curves Speaker: Benedict Gross, Harvard University Date and Time: Tuesday, November 1, 2016 - 10:00am to 11:00am Location: Fields Institute, Room 230 Abstract: One of Manjul Bhargava's most surprising results in arithmetic geometry is his proof that mos

From playlist Mathematics

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Alena Pirutka: On examples of varieties that are not stably rational

Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b

From playlist Algebraic and Complex Geometry

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Rahim Moosa 5/13/16 Part 1

Title: The Dixmier-Moeglin Problem for D-Varieties May 2016 Kolchin Seminar Workshop

From playlist May 2016 Kolchin Seminar Workshop

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Sebastian Falkensteiner, Max Planck Institute for Mathematics in the Sciences

March 10, Sebastian Falkensteiner, Max Planck Institute for Mathematics in the Sciences Transforming radical differential equations into algebraic differential equations

From playlist Spring 2023 Online Kolchin Seminar in Differential Algebra

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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

Related pages

Quartic threefold | Birational geometry | Galois theory | Dimension of an algebraic variety | Rational function | Zariski surface | Fixed point (mathematics) | Indeterminate (variable) | Transcendence degree | Algebraic variety | Severi–Brauer variety | Cubic surface | Function field of an algebraic variety | Projective space | Rational surface | Hypersurface | Intermediate Jacobian | Finite group | Field extension | Projective line | Mathematics | Field (mathematics) | Riemann–Hurwitz formula | Arithmetic genus | Moduli space