Topic
Rational surface
About: Rational surface is a research topic. Over the lifetime, 436 publications have been published within this topic receiving 8328 citations.
Papers published on a yearly basis
Papers
TL;DR: In this article, a geometric approach to the theory of Painleve equations based on rational surfaces is presented, where a compact smooth rational surface X has a unique anti-canonical divisor D of canonical type.
Abstract: We present a geometric approach to the theory of Painleve equations based on rational surfaces Our starting point is a compact smooth rational surface X which has a unique anti-canonical divisor D of canonical type We classify all such surfaces X To each X, there corresponds a root subsystem of E
(1)
8 inside the Picard lattice of X We realize the action of the corresponding affine Weyl group as the Cremona action on a family of these surfaces We show that the translation part of the affine Weyl group gives rise to discrete Painleve equations, and that the above action constitutes their group of symmetries by Backlund transformations The six Painleve differential equations appear as degenerate cases of this construction In the latter context, X is Okamoto's space of initial conditions and D is the pole divisor of the symplectic form defining the Hamiltonian structure
703 citations
TL;DR: In this article, the self-consistent classical plasma equilibrium with diffusion was studied in a toroidal geometry having a sheared magnetic field and it was found that the pressure gradient is zero unless the Fourier component of 1/B2, which resonates with that surface, vanishes.
Abstract: The self‐consistent classical plasma equilibrium with diffusion is studied in a toroidal geometry having a sheared magnetic field. Near each rational surface it is found that the pressure gradient is zero unless the Fourier component of 1/B2, which resonates with that surface, vanishes. Despite the resonances, the overall plasma confinement is, in practice, only slightly modified by the rational surfaces.
436 citations
TL;DR: A theorem on rational parametrizations for envelopes of natural quadrics leads to algorithms for the computation of rational parammetrizations of surfaces; those include canal surfaces with rational spine curve and rational radius function, offsets of rational ruled surfaces or quadrics, and surfaces generated by peripheral milling with a cylindrical or conical cutter.
159 citations
TL;DR: In this article, a determination of the fixed components, base points and irregularity of any smooth projective rational surface having an effective anticanonical divisor is made.
Abstract: A determination of the fixed components, base points and irregularity is made for arbitrary numerically effective divisors on any smooth projective rational surface having an effective anticanonical divisor. All of the results are proven over an algebraically closed field of arbitrary characteristic. Applications, treated in separate papers, include questions involving: points in good position, birational models of rational surfaces in projective space, and resolutions for ideals of fat point subschemes of $P^2$.
115 citations
102 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 1 |
| 2024 | 2 |
| 2023 | 8 |
| 2022 | 29 |
| 2021 | 14 |
| 2020 | 11 |