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In mathematics, a '''Burniat surface''' is one of the [[surfaces of general type]] introduced by {{harvs|txt|last=Burniat|first=Pol|year=196 ...t3=Chris A.M. | last4=Van de Ven | first4=Antonius | title=Compact Complex Surfaces | publisher= Springer-Verlag, Berlin | series=Ergebnisse der Mathematik und ...

...ich are in fact [[quartic curve]]s over {{tmath|\mathbb{C} }}, and quartic surfaces over {{tmath|\mathbb{R} }}. For instance, the [[Klein quartic]] is a ''real ==Special quartic surfaces== ...

...ines. The term "Segre surface" is also occasionally used for various other surfaces, such as a quadric in 3-dimensional projective space, or the hypersurface *{{Citation | last1=Segre | first1=Corrado | title=Etude des différentes surfaces du 4^e ordre à conique double ou cuspidale (générale ou décomposé ...

...Châtelet (mathematician)| title=Points rationnels sur certaines courbes et surfaces cubiques | url=http://retro.seals.ch/digbib/view?rid=ensmat-001:1959:5::55 ...mr=2914907|pages=231–236|title=Failure of the Hasse principle for Châtelet surfaces in characteristic 2|url=https://jtnb.cedram.org/item?id=JTNB_2012__24_1_231 ...

...ra theorem, valid in algebraic geometry over the complex numbers, has such surfaces as counterexamples, and these can only exist in [[characteristic p|characte ...ud surfaces''' were introduced in {{harv|Lang|1983}}, and give examples of surfaces of general type with global vector fields. ...

In mathematics, a '''Catanese surface''' is one of the [[surfaces of general type]] introduced by {{harvs|txt|last=Catanese|first=Fabrizio|au ...ere is a group of order 5 [[free group action|acting freely]] on all these surfaces, then the quotient ''Z'' of ''Y'' by this group of order 5 is a Catanese su ...

...-trivial examples of Kodaira class VII surfaces in 1974.<ref>M. Inoue, "On surfaces of class VII₀," ''Inventiones math.'', 24 (1974), 269–310.</ref> The Inoue surfaces are not [[Kähler manifold]]s. ...

...uclidean space]]. It is named after [[Edmond Bour]], whose work on minimal surfaces won him the 1861 mathematics prize of the French Academy of Sciences.<ref>{ ...ion]].<ref>Ulrich Dierkes, Stefan Hildebrandt, Friedrich Sauvigny, Minimal Surfaces, Volume 1. Springer 2010</ref> ...

...et]] family) of a [[minimal surface]] is a one-parameter family of minimal surfaces which share the same [[Weierstrass–Enneper parameterization|Weierstrass dat where <math>\Re</math> indicates the real part of a [[complex number]]. ...

Sarti has also found sextic, octic and dodectic nodal surfaces with high numbers of nodes and high degrees of symmetry. | title = Pencils of symmetric surfaces in <math>\mathbb{P}_3</math> ...

...& Tibor Radó, World Scientific, 1992 (p. 239-240)</ref> It is a family of surfaces with one planar [[End (topology)|end]] and one [[Enneper surface]]-like sel ...math>f(z)=1/z^2, g(z)=z^m</math>. This allows a parametrization based on a complex parameter as ...

In mathematics, '''Dolgachev surfaces''' are certain [[simply connected space|simply connected]] [[elliptic surfa The Dolgachev surfaces are simply connected, and the bilinear form on the second [[cohomology grou ...

{{for|nodal surfaces in physics and chemistry|Node (physics)}} ...a '''nodal surface''' is a surface in (usually [[Complex projective space|complex]]) [[projective space]] whose only singularities are [[Singular_point_of_an ...

...gebraic geometry|pages=23–42|year=1977|chapter=Enriques' classification of surfaces in char. p. II|location=Tokyo|publisher=Iwanami Shoten|mr=0491719|last2=Mum ...ometric genus]] and the [[arithmetic genus]] of more complicated surfaces. Surfaces are sometimes called regular or irregular depending on whether or not the i ...

*[[List of algebraic surfaces]] ...p://enriques.mathematik.uni-mainz.de/docs/Etogliatti.shtml|title=Togliatti surfaces|first=Stephan |last=Endraß|year=2003}} ...

The problem can be solved by extending the surface from the curve using complex [[analytic continuation]]. If <math>c(s)</math> is a real analytic curve in ...al Surfaces as Isotropic Curves in '''C'''³: Associated minimal surfaces and the Björling's problem. MIT BA Thesis. 2004 http://ocw.mit.edu/courses/ ...

...topological [[4-manifold]]. It holds more generally for minimal projective surfaces of general type over an algebraically closed field. ...efined over an [[algebraically closed field]] (or a smooth minimal compact complex surface of general type) with canonical divisor ''K'' = −''c''₁( ...

...re not used to represent physical positions, like an [[affine plane]] or [[complex plane]]. ...iemannian surfaces]]. (Not to be confused with [[Riemann surfaces]].) Some surfaces are [[Embedding|embedded]] in [[three-dimensional Euclidean space]] or some ...

...cyclides are a [[superset]] of [[Dupin cyclide]]s and [[quadric]]s. These surfaces have applications in [[architectural geometry]] and [[computer-aided geomet ...s equation factors into non-constant polynomials with [[complex polynomial|complex coefficients]], the Darboux cyclide is called a ''reducible'' cyclide. A re ...

== Complex analysis == ...the [[complex plane]] with its standard flat metric. In this situation a complex-valued [[function (mathematics)|function]] <math>\phi=u+iv:(M,g)\to\mathbb ...