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Cubic surface

In mathematics, a cubic surface is a surface in 3-dimensional space defined by one polynomial equation of degree 3. Cubic surfaces are fundamental examples in algebraic geometry. The theory is simplified by working in projective space rather than affine space, and so cubic surfaces are generally considered in projective 3-space P 3 {\displaystyle \mathbf…

27 lines on a cubic surface, Rationality of cubic surfaces & Cubic surfaces over a field

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Overview

Rationality of cubic surfaces

27 lines on a cubic surface

Special cubic surfaces

Real cubic surfaces

Moduli spaces of cubic surfaces

The cone of curves

Cubic surfaces over a field

Singular cubic surfaces

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Map overview Semantic statistics

Cubic surface

Nodes108
Edges107
Triples234
Avg. degree1.98
Density0.018519
Components1

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Cubic surface

Top relations

related to References · 117
Cubic surface → AG, Alessio, Alexei, Algebra, Algebraic, Amsterdam, An, Applications, Archibald, Arthur, Beniamino, BFb0088815, Bruce, Cambridge, Cambridge Tracts, Cambridge University Press, CBO9780511734991, CBO9781139084437, Classical, Compact
related to Cubic surfaces over a field · 18
Cubic surface → As, Beniamino Segre, For, Galois, If, In, János Kollár, More, Otherwise, Pezzo, Pic, Picard, Segre, The, The Picard, Weyl, Yuri Manin, Zariski
related to Moduli spaces of cubic surfaces · 18
Cubic surface → By, Clebsch, Du Val, Further, Geometric, GIT, Hacking, In, K-moduli, Keel, KSBA-stable, More, Pezzo, Salmon, Tevelev, The, This, Two
related to 27 lines on a cubic surface · 17
Cubic surface → Another, Arthur Cayley, Arthur Coble, As, Cartan, George Salmon, Grassmannian, In, Lie, More, Most, Patrick, Schubert, The, This, Val, Weyl
related to External links · 16
Cubic surface → Cubic, DVD, Edmund, John, MacTutor History, Maryland, Mathematics Archive, O'Connor, Robertson, Ryan Hoban, St AndrewsLines, The Cubic Surfaces DVD, The Experimental Geometry Lab, The Wolfram Demonstrations Project, University, William Goldman
related to The cone of curves · 10
Cubic surface → Also, For, In, Pezzo, Pic, Picard, The, There, This, Weyl
related to Rationality of cubic surfaces · 8
Cubic surface → Alfred Clebsch, As, Clebsch, Conversely, CP, In, More, That
related to Real cubic surfaces · 8
Cubic surface → Felix Klein, In, Its, Ludwig Schläfli, Namely, RP, The, Zeuthen
related to Automorphism groups of singular cubic surfaces with no parameters · 5
Cubic surface → An, If, Moreover, Such, The
related to Classification · 5
Cubic surface → Depending, In, Notice, That, The

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Important terminology

cubic displaystyle surfaces surface lines smooth mathbf group 27 space singular rational real automorphism points doi isomorphic mr algebraic complex

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Cubic surfaceis asurface in 3-dimensional space defined by one polynomial equation of degree 30.90text
Cubic surfaceis aClebsch surface0.90text
Cubic surfaceis aunique surface with the maximal number of nodes0.90text
the Schläfli double six configurationinstance ofThis graph was analyzed in the 19th century using subgraphs0.80text
Cubic surfacerelated to 27 lines on a cubic surfaceMost0.60section
Cubic surfacerelated to 27 lines on a cubic surfaceIn0.60section
Cubic surfacerelated to 27 lines on a cubic surfaceMore0.60section
Cubic surfacerelated to 27 lines on a cubic surfaceArthur Cayley0.60section
Cubic surfacerelated to 27 lines on a cubic surfaceGeorge Salmon0.60section
Cubic surfacerelated to 27 lines on a cubic surfaceThis0.60section
Cubic surfacerelated to 27 lines on a cubic surfaceAnother0.60section
Cubic surfacerelated to 27 lines on a cubic surfaceSchubert0.60section

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