Ad
related to: algebraic surfaces milano italy map images of homes for rentspotahome.com has been visited by 10K+ users in the past month
Search results
Results from the WOW.Com Content Network
In algebraic geometry, a Togliatti surface is a nodal surface of degree five with 31 nodes. The first examples were constructed by Eugenio G. Togliatti ( 1940 ). Arnaud Beauville ( 1980 ) proved that 31 is the maximum possible number of nodes for a surface of this degree, showing this example to be optimal.
In algebraic geometry, a branch of mathematics, a Zariski surface is a surface over a field of characteristic p > 0 such that there is a dominant inseparable map of degree p from the projective plane to the surface. In particular, all Zariski surfaces are unirational.
Quotient surfaces, surfaces that are constructed as the orbit space of some other surface by the action of a finite group; examples include Kummer, Godeaux, Hopf, and Inoue surfaces; Zariski surfaces, surfaces in finite characteristic that admit a purely inseparable dominant rational map from the projective plane
An algebraic surface is an algebraic variety of dimension two. The Enriques-Kodaira classification gives an overview of the possibilities. Over the complex numbers , a non-singular algebraic surface is an example of a 4-manifold .
The emphasis on algebraic surfaces—algebraic varieties of dimension two—followed on from an essentially complete geometric theory of algebraic curves (dimension 1). The position in around 1870 was that the curve theory had incorporated with Brill–Noether theory the Riemann–Roch theorem in all its refinements (via the detailed geometry of the theta-divisor).
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems. Classically, it studies zeros of multivariate polynomials ; the modern approach generalizes this in a few different aspects.
Basic results on algebraic surfaces include the Hodge index theorem, and the division into five groups of birational equivalence classes called the classification of algebraic surfaces. The general type class, of Kodaira dimension 2, is very large (degree 5 or larger for a non-singular surface in P 3 lies in it, for example).
By well known results on a cubic surface, the number of lines that cuts two disjoints lines is 5, thus we get (C s) 2 =C s C t =5. As K is numerically equivalent to 3C s, we obtain K 2 =45. c) The natural composite map: S -> G(2,5) -> P 9 is the canonical map of S. It is an embedding.
Ad
related to: algebraic surfaces milano italy map images of homes for rentspotahome.com has been visited by 10K+ users in the past month