In mathematics, the irregularity of a complex surface X is the Hodge number , usually denoted by q.[1] The irregularity of an algebraic surface is sometimes defined to be this Hodge number, and sometimes defined to be the dimension of the Picard variety, which is the same in characteristic 0 but can be smaller in positive characteristic.[2]
The name "irregularity" comes from the fact that for the first surfaces investigated in detail, the smooth complex surfaces in P3, the irregularity happens to vanish. The irregularity then appeared as a new "correction" term measuring the difference of the geometric genus and the arithmetic genus of more complicated surfaces. Surfaces are sometimes called regular or irregular depending on whether or not the irregularity vanishes.
For a complex analytic manifold X of general dimension, the Hodge number is called the irregularity of , and is denoted by q.
^Barth, Wolf P.; Hulek, Klaus; Peters, Chris A.M.; Van de Ven, Antonius (2004), Compact Complex Surfaces, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge., vol. 4, Springer-Verlag, Berlin, ISBN 978-3-540-00832-3, MR 2030225
^Bombieri, Enrico; Mumford, David (1977), "Enriques' classification of surfaces in char. p. II", Complex analysis and algebraic geometry, Tokyo: Iwanami Shoten, pp. 23–42, MR 0491719
and 27 Related for: Irregularity of a surface information
In mathematics, the irregularityofa complex surface X is the Hodge number h 0 , 1 = dim H 1 ( O X ) {\displaystyle h^{0,1}=\dim H^{1}({\mathcal {O}}_{X})}...
an irregularity is an impediment for the Catholic priesthood or for exercising orders already received IrregularityofasurfaceIrregularityof distributions...
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for surfaces is called the irregularityofasurface. In terms of differential forms, any holomorphic 1-form on V {\displaystyle V} is a pullback of translation-invariant...
provide enough energy to form stable nuclei. In presence ofirregularities on the surfaceof the containing vessel, solid or gaseous impurities, pre-formed...
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as chocolate coated peanuts. Irregularities on the surfaceof the product being sprayed may result in the formation of unsightly aggregates ("lac-aggs")...
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highest hardness of any bulk material, and uses diamond tools to smooth out bumps and other irregularities on the surface. Diamond grinding of pavement Diamond...
level of abstraction; it does not provide an exact distance, which is unattainable if one attempted to account for every irregularity in the surfaceof the...
12q\geqslant 0} where q is the irregularityofasurface (the Noether inequality). Many (and possibly all) pairs of integers satisfying these conditions...
canonical bundle and irregularity zero. An (algebraic) K3 surface over any field means a smooth proper geometrically connected algebraic surface that satisfies...
from its runway. A ground collision occurs when an aircraft collides with another aircraft and/or structure on the runway. lack of sufficient training...
correct corneal scarring, thinning, or surfaceirregularity. There is currently limited data on long-term survival of DMEK grafts however the early indications...
must be considered: a smooth projectile will face less air resistance than a rough-surfaced one, and irregularities on the surfaceofa projectile may change...
{\displaystyle 5c_{1}(X)^{2}-c_{2}(X)+36\geq 12q} where q is the irregularityofasurface, which leads to a slightly weaker inequality, which is also often called...
differential diagnosis. Imaging such as the use of an x-ray can reveal irregularitiesof the surfacesof the lower ribs and iliac crest or abnormally long...
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in combination with irregularities in the surfaceof the runway, that led the left main gear to leave the ground before rotation. A funeral procession...
or through a channel. All of these measures ultimately derive from frictional forces, which result from irregularities on the surfacesof relevance.[citation...
allows for minor irregularities in the surface. The slope may be provided by the floor, or benches or racks that hold the channels. As a general guide,...
of the film. This configuration is used in most practical applications. When the surface plasmon wave interacts with a local particle or irregularity...
involutions. irregularity The irregularityofasurface is the dimension of the space of holomorphic 1-forms on a non-singular projective surface; see Hodge...
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