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Algebraic surface

In mathematics, an algebraic surface is an algebraic variety of dimension two. Thus, an algebraic surface is a solution of a set of polynomial equations, in which there are two independent directions at every point. An example of an algebraic surface is the sphere, which is determined by the single polynomial equation x 2 + y 2 + z 2 = 1. {\displaystyle…

Classification by the Kodaira dimension, Properties & Overview

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Classification by the Kodaira dimension

Birational geometry of surfaces

Properties

Riemann-Roch theorem for surfaces

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Algebraic surface

Nodes66
Edges65
Triples36
Avg. degree1.97
Density0.030303
Components1

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Algebraic surface

Top relations

related to References · 16
Algebraic surface → Algebraic, Berlin, Classics, Dolgachev, EMS PressZariski, Encyclopedia, ISBN, Lock-gray-alt-2, Lock-green, Lock-red-alt-2, Mathematics, MR, New York, Oscar, Springer-Verlag, Wikisource-logo
related to External links · 6
Algebraic surface → Algebraic, Algebraic Surfaces, Free, Page, SingSurf, SURFER
related to Classification by the Kodaira dimension · 4
Algebraic surface → Examples, In, Kodaira, Then
is a · 3
Algebraic surface → algebraic variety of dimension two, solution of a set of polynomial equations, sphere
related to Castelnuovo's Theorem · 3
Algebraic surface → Castelnuovo's, One, This
related to Birational geometry of surfaces · 2
Algebraic surface → Certain, The

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Important terminology

algebraic surfaces surface curves dimension two geometry displaystyle example complex theorem classification may birational one also hodge point much sphere

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Algebraic surfaceis aalgebraic variety of dimension two0.90text
Algebraic surfaceis asolution of a set of polynomial equations0.90text
Algebraic surfaceis asphere0.90text
it is the pullback of some hyperplane bundle of projective spaceinstance of0.Ample divisors have a nice property0.80text
whose properties are very well knowninstance of0.Ample divisors have a nice property0.80text
Algebraic surfacerelated to Birational geometry of surfacesThe0.60section
Algebraic surfacerelated to Birational geometry of surfacesCertain0.60section
Algebraic surfacerelated to Castelnuovo's TheoremOne0.60section
Algebraic surfacerelated to Castelnuovo's TheoremCastelnuovo's0.60section
Algebraic surfacerelated to Castelnuovo's TheoremThis0.60section
Algebraic surfacerelated to Classification by the Kodaira dimensionIn0.60section
Algebraic surfacerelated to Classification by the Kodaira dimensionThen0.60section

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