Algebraic surfaces

Algebraic surface

In mathematics, an algebraic surface is an algebraic variety of dimension two. In the case of geometry over the field of complex numbers, an algebraic surface has complex dimension two (as a complex manifold, when it is non-singular) and so of dimension four as a smooth manifold. The theory of algebraic surfaces is much more complicated than that of algebraic curves (including the compact Riemann surfaces, which are genuine surfaces of (real) dimension two). Many results were obtained, however, in the Italian school of algebraic geometry, and are up to 100 years old. (Wikipedia).

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Algebraic Expressions (Basics)

This video is about Algebraic Expressions

From playlist Algebraic Expressions and Properties

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Complex surfaces 1: Introduction

This talk is part of a series giving an informal survey of complex algebraic surfaces. We give an overview of the Enriques-Kodaira classification, with examples of most of the different types of surfaces. We conclude by giving an example of a non-algebraic surface: the Hopf surface. Furth

From playlist Algebraic geometry: extra topics

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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

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Homotopy animation

An interesting homotopy (in fact, an ambient isotopy) of two surfaces.

From playlist Algebraic Topology

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Unipotent structures of algebraic varieties by Masayoshi Miyanshi

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

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Unipotent structures of algebraic varieties by Masayoshi Miyanshi

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

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On a quadratic plane by S. M. Bhatwadekar

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

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MATH331: Riemann Surfaces - part 1

We define what a Riemann Surface is. We show that PP^1 is a Riemann surface an then interpret our crazy looking conditions from a previous video about "holomorphicity at infinity" as coming from the definition of a Riemann Surface.

From playlist The Riemann Sphere

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Complex surfaces 2: Minimal surfaces

This talk is part of a series about complex surfaces, and explains what minimal surfaces are. A minimial surfaces is one that cannot be obtained by blowing up a nonsingular surfaces at a point. We explain why every surface is birational to a minimal nonsingular projective surface. We disc

From playlist Algebraic geometry: extra topics

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A geometric model for the bounded derived category of a gentle algebra, Sibylle Schroll, Lecture 1

Gentle algebras are quadratic monomial algebras whose representation theory is well understood. In recent years they have played a central role in several different subjects such as in cluster algebras where they occur as Jacobian algebras of quivers with potentials obtained from triangula

From playlist Winter School on “Connections between representation Winter School on “Connections between representation theory and geometry"

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A geometric model for the bounded derived category of a gentle algebra, Sibylle Schroll Lecture 3

Gentle algebras are quadratic monomial algebras whose representation theory is well understood. In recent years they have played a central role in several different subjects such as in cluster algebras where they occur as Jacobian algebras of quivers with potentials obtained from triangula

From playlist Winter School on “Connections between representation Winter School on “Connections between representation theory and geometry"

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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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Pierrick Bousseau - The Skein Algebra of the 4-punctured Sphere from Curve Counting

The Kauffman bracket skein algebra is a quantization of the algebra of regular functions on the SL_2 character of a topological surface. I will explain how to realize the skein algebra of the 4-punctured sphere as the output of a mirror symmetry construction based on higher genus Gromov-Wi

From playlist 2021 IHES Summer School - Enumerative Geometry, Physics and Representation Theory

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Joakim Arnlind - Discrete Minimal Surface Algebras

https://indico.math.cnrs.fr/event/4272/attachments/2260/2714/IHESConference_Joakim-ARNLIND.pdf

From playlist Space Time Matrices

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Juliet Cooke: Skein categories

In this talk we will talk about skein categories which are a categorical analogue of skein algebras based on coloured ribbon tangles. We shall then see how these skein categories satisfy excision and therefore fit within the framework of factorisation homology as k-linear factorisation hom

From playlist Workshop: Monoidal and 2-categories in representation theory and categorification

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A Tour of Skein Modules by Rhea Palak Bakshi

PROGRAM KNOTS THROUGH WEB (ONLINE) ORGANIZERS: Rama Mishra, Madeti Prabhakar, and Mahender Singh DATE & TIME: 24 August 2020 to 28 August 2020 VENUE: Online Due to the ongoing COVID-19 pandemic, the original program has been canceled. However, the meeting will be conducted through onl

From playlist Knots Through Web (Online)

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Hodge theory and algebraic cycles - Phillip Griffiths

Geometry and Arithmetic: 61st Birthday of Pierre Deligne Phillip Griffiths Institute for Advanced Study October 18, 2005 Pierre Deligne, Professor Emeritus, School of Mathematics. On the occasion of the sixty-first birthday of Pierre Deligne, the School of Mathematics will be hosting a f

From playlist Pierre Deligne 61st Birthday

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An introduction to surfaces | Differential Geometry 21 | NJ Wildberger

We introduce surfaces, which are the main objects of interest in differential geometry. After a brief introduction, we mention the key notion of orientability, and then discuss the division in the subject between algebraic surfaces and parametrized surfaces. It is very important to have a

From playlist Differential Geometry

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Complex surfaces 5: Kodaira dimension 0

This talk is an informal survey of the complex projective surfaces of Kodaira number 0. We first explain why there are 4 types of such surfaces (Enriques, K3, hyperelliptic, and abelian) and then give a few examples of each type.

From playlist Algebraic geometry: extra topics

Related pages

Birational geometry | Dimension of an algebraic variety | Rational function | Hodge cycle | Max Noether | Algebraic variety | Complex projective plane | Irregularity of a surface | Del Pezzo surface | Complex manifold | Castelnuovo's contraction theorem | Cubic surface | Hyperelliptic surface | Italian school of algebraic geometry | Function field of an algebraic variety | Ample line bundle | Weil conjectures | Kodaira dimension | Abelian surface | K3 surface | Geometric genus | Projective line | Riemann surface | Mathematics | Veronese surface | Arithmetic genus | Elliptic surface | Hodge index theorem | Intersection number | Blowing up | Ruled surface | Birational invariant | Compact space | Quadratic form | Surface of general type | Algebraic curve | Complex number | Projective plane | Surface (topology) | Quadric | Enriques surface