Algebraic curves

Real hyperelliptic curve

There are two types of hyperelliptic curves, a class of algebraic curves: real hyperelliptic curves and imaginary hyperelliptic curves which differ by the number of points at infinity. Hyperelliptic curves exist for every genus . The general formula of Hyperelliptic curve over a finite field is given by where satisfy certain conditions. In this page, we describe more about real hyperelliptic curves, these are curves having two points at infinity while imaginary hyperelliptic curves have one point at infinity. (Wikipedia).

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Hyperbola 3D Animation | Objective conic hyperbola | Digital Learning

Hyperbola 3D Animation In mathematics, a hyperbola is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, that are mirror images of each other an

From playlist Maths Topics

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What is the definition of a hyperbola

Learn all about hyperbolas. A hyperbola is a conic section with two fixed points called the foci such that the difference between the distances of any point on the hyperbola from the two foci is equal to the distance between the two foci. Some of the characteristics of a hyperbola includ

From playlist The Hyperbola in Conic Sections

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What is the definition of a hyperbola

Learn all about hyperbolas. A hyperbola is a conic section with two fixed points called the foci such that the difference between the distances of any point on the hyperbola from the two foci is equal to the distance between the two foci. Some of the characteristics of a hyperbola includ

From playlist The Hyperbola in Conic Sections

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Ex 1: Conic Section - Graph a Hyperbola with Center at the Origin (Horizontal)

This video provides an example of how to graph and find the major components of a hyperbola given the standard equation of the hyperbola. The hyperbola has a horizontal transverse axis. Site: http:/mathispower4u.com Blog: http://mathispower4u.wordpress.com

From playlist Graphing and Writing Equations of Hyperbolas

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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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What are the equations for a hyperbolas with a horizontal and vertical transverse axis

Learn all about hyperbolas. A hyperbola is a conic section with two fixed points called the foci such that the difference between the distances of any point on the hyperbola from the two foci is equal to the distance between the two foci. Some of the characteristics of a hyperbola includ

From playlist The Hyperbola in Conic Sections

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Most Hyperelliptic Curves Over Q Have No Rational Points - Manjul Bhargava

Manjul Bhargava Princeton University April 18, 2013 For more videos, visit http://video.ias.edu

From playlist Mathematics

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Umberto Zannier - Ambients for the Betti map and the question of its rank

November 16, 2017 - This is the final talk of a series of three Fall 2017 Minerva Lectures In this last lecture we shall further consider some of the mentioned contexts involving the Betti map. We shall also discuss in short some recent work with Yves André and Pietro Corvaja, where we obt

From playlist Minerva Lectures Umberto Zannier

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Writing the standard form of a hyperbola given the foci and asymptotes

Learn how to write the equation of hyperbolas given the characteristics of the hyperbolas. The standard form of the equation of a hyperbola is of the form: (x - h)^2 / a^2 - (y - k)^2 / b^2 = 1 for horizontal hyperbola or (y - k)^2 / a^2 - (x - h)^2 / b^2 = 1 for vertical hyperbola. The c

From playlist The Hyperbola in Conic Sections

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Algebra Ch 40: Hyperbolas (1 of 10) What is a Hyperbola?

Visit http://ilectureonline.com for more math and science lectures! To donate: http://www.ilectureonline.com/donate https://www.patreon.com/user?u=3236071 We will learn a hyperbola is a graph that result from meeting the following conditions: 1) |d1-d2|=constant (same number) 2) the grap

From playlist THE "HOW TO" PLAYLIST

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Rachel Pries - The geometry of p-torsion stratifications of the moduli space of curve

The geometry of p-torsion stratifications of the moduli space of curve

From playlist 28ème Journées Arithmétiques 2013

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CTNT 2020 - Semistable models of hyperelliptic curves over residue characteristic 2 - Jeffrey Yelton

The Connecticut Summer School in Number Theory (CTNT) is a summer school in number theory for advanced undergraduate and beginning graduate students, to be followed by a research conference. For more information and resources please visit: https://ctnt-summer.math.uconn.edu/

From playlist CTNT 2020 - Conference Videos

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Nicholas Triantafillou, Computing isolated points on modular curves

VaNTAGe seminar, on Nov 10, 2020 License: CC-BY-NC-SA.

From playlist ICERM/AGNTC workshop updates

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How to determine the parts of a hyperbola and then sketch the graph

Learn how to graph hyperbolas. To graph a hyperbola from the equation, we first express the equation in the standard form, that is in the form: (x - h)^2 / a^2 - (y - k)^2 / b^2 = 1 for horizontal hyperbola or (y - k)^2 / a^2 - (x - h)^2 / b^2 = 1 for vertical hyperbola. Next, we identify

From playlist The Hyperbola in Conic Sections

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Given vertices and asymptotes, write the equation of the hyperbola

Learn how to write the equation of hyperbolas given the characteristics of the hyperbolas. The standard form of the equation of a hyperbola is of the form: (x - h)^2 / a^2 - (y - k)^2 / b^2 = 1 for horizontal hyperbola or (y - k)^2 / a^2 - (x - h)^2 / b^2 = 1 for vertical hyperbola. The c

From playlist The Hyperbola in Conic Sections

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Andrew Sutherland, Arithmetic L-functions and their Sato-Tate distributions

VaNTAGe seminar on April 28, 2020. License: CC-BY-NC-SA Closed captions provided by Jun Bo Lau.

From playlist The Sato-Tate conjecture for abelian varieties

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Riemann Roch: genus 2 curves

This talk is about the Riemann-Roch theorem for genus 2 curves. We show that all genus 2 complex curves are hyperelliptic (meaning they are branched double covers of the projective line). We also describe the Weierstrass points and the holomorphic 1-forms explicitly. Finally we briefly su

From playlist Algebraic geometry: extra topics

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Given the vertices and foci write the standard form of a hyperbola

Learn how to write the equation of hyperbolas given the characteristics of the hyperbolas. The standard form of the equation of a hyperbola is of the form: (x - h)^2 / a^2 - (y - k)^2 / b^2 = 1 for horizontal hyperbola or (y - k)^2 / a^2 - (x - h)^2 / b^2 = 1 for vertical hyperbola. The c

From playlist The Hyperbola in Conic Sections

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Algebraic geometry 44: Survey of curves

This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It gives an informal survey of complex curves of small genus.

From playlist Algebraic geometry I: Varieties

Related pages

Hyperelliptic curve | Algebraic curve | Elliptic curve | Algebraic closure | Partial derivative | Abelian group | Imaginary hyperelliptic curve | Homogeneous coordinates | Blowing up