On rational surfaces, II

@inproceedings{Nagata1960OnRS,
  title={On rational surfaces, II},
  author={Masayoshi Nagata},
  year={1960}
}
In § 1 of the present paper, we introduce the notion of a virtual linear system on a non-singular projective surface and we clarify the theories o f infinitely near points, of divisors and o f linear system with preassigned base conditions. We introduce in § 2 the notions of a numerical types and of non-special points with respect to Cremona transformations. They play important roles in § 3 in order to prove characterizations and existence theorems o f exceptional curves of the first kind and… 

A pr 2 00 1 EXISTENCE OF CURVES WITH PRESCRIBED TOPOLOGICAL SINGULARITIES

Throughout this paper we study the existence of irreducible curves C on smooth projective surfaces Σ with singular points of prescribed topological types S 1 ,. .. , S r. There are necessary

Complete linear systems on rational surfaces

We determine the dimension, fixed components and base points of complete linear systems on blowings-up of P2 having irreducible anticanonical divisor. Consider a set of pointspx,...,p„ of the

RATIONAL SURFACES OVER PERFECT FIELDS. II

Letk be a perfect field of arbitrary characteristic. The main object of this paper is to establish some new objects associated with algebraic surfaces F defined overk which are invariants for

Linear systems on a special rational surface

We study the Hilbert series of a family of ideals J_\phi generated by powers of linear forms in k[x_1,...,x_n]. Using the results of Emsalem-Iarrobino, we formulate this as a question about fatpoints

On finiteness of curves with high canonical degree on a surface

The canonical degree of a curve C on a surface X is $$K_X\cdot C$$KX·C. Our main result, Theorem 1.1, is that on a surface of general type there are only finitely many curves with negative

Plane Cremona maps, exceptional curves and roots

We address three different questions concerning exceptional and root divisors (of arithmetic genus zero and of self-intersection -1 and -2, respectively) on a smooth complex projective surface S

THE GEOMETRY OF RATIONAL SURFACES AND HILBERT FUNCTIONS OF POINTS IN THE PLANE

We study the structure of the set of numerically effective divisor classes on a rational surface and apply this to study hilbert functions of the homogeneous coordinate rings of 0-cycles on curves of

2 6 M ar 2 00 2 The Projective Theory of Ruled Surfaces

Introduction: Through this paper, a geometrically ruled surface, or simply a ruled surface, will be a P-bundle over a smooth curve X of genus g. It will be denoted by π : S = P(E0)−→X and we will
...

References

SHOWING 1-8 OF 8 REFERENCES

Algebraic Geometry and Theta Functions

  • H. P.
  • Mathematics
    Nature
  • 1930

Franchetta, Sulle curve eccezionali di prima specie appartenenti ad una superficie algebrica

  • Boll. Un. Mat. Ital.,
  • 1940

Recerche generali sopra i systemi lineari d i curve piani, Mem

  • Accad. Sci. Torino,
  • 1892

On the 14-th Problem of Hilbert

Recerche generali sopra i systemi lineari d i curve piani

  • Mem. Accad. Sci. Torino, ser

Sulle curve eccezionali di prim a specie appartenenti ad una superficie algebrica

  • Boll. Un. M at. Ital., ser

Sulla caratterizzatione delle curve eccezionali riducibili di prima specie, ibid

    Z a ris k i, Introduction t o th e problem of m inim al models in th e theory of algebraic surfaces

    • 1958