Minimal degree rational curves on real surfaces
- MathematicsAdvances in Mathematics
Clifford and Euclidean translations of circles
- Mathematics, Physics
Celestials are surfaces that contain at least two real circles through a general point. We present a partial classification of celestials in the three-sphere up to Moebius equivalence. In particular,…
Computing basepoints of linear series in the plane
- Mathematics, Computer ScienceArXiv
An algorithm for detecting basepoints of linear series of curves in the plane of classical procedure of blowing up points in the planes is presented and the algorithmic version of this procedure with several applications is motivated.
SHOWING 1-10 OF 19 REFERENCES
The parametric degree of a rational surface
The parametric degree of a rational surface is the degree of the polynomials in the smallest possible proper parametrization. An example shows that the parametric degree is not a geometric but an…
Lattice polygons and families of curves on rational surfaces
First we solve the problem of finding minimal degree families on toric surfaces by reducing it to lattice geometry. Then we describe how to find minimal degree families on, more generally, rational…
Minimal families of curves on surfaces
Principles of Algebraic Geometry
A comprehensive, self-contained treatment presenting general results of the theory. Establishes a geometric intuition and a working facility with specific geometric practices. Emphasizes applications…
An inequality for adjoint rational surfaces
We generalize an inequality for convex lattice polygons -- aka toric surfaces -- to general rational surfaces.
Complex Algebraic Surfaces
- Mathematics, Chemistry
Introduction Notation Part I. The Picard Group and the Riemann-Roch Theorem: Part II. Birational Maps: Part III. Ruled Surfaces: Part IV. Rational Surfaces: Part V. Castelnuovo's Theorem and…
Moving Out the Edges of a Lattice Polygon
- Mathematics, Computer ScienceDiscret. Comput. Geom.
The dual operations of taking the interior hull and moving out the edges of a two-dimensional lattice polygon are reviewed and it is shown how the latter operation naturally gives rise to an algorithm for enumerating lattice polygons by their genus.
Lattice Polygons and the Number 2i + 7
- MathematicsAm. Math. Mon.
The authors came up with new inequalities: Scott's inequality can be sharpened if one takes into account another invariant, which is de fined by peeling off the skins of the polygons like an onion (see Section 3).
Classical setting : line bundles and linear series
Notation and Conventions.- One: Ample Line Bundles and Linear Series.- to Part One.- 1 Ample and Nef Line Bundles.- 2 Linear Series.- 3 Geometric Manifestations of Positivity.- 4 Vanishing Theorems.-…