Pseudo-Riemann’s quartics in Finsler’s geometry—two-dimensional case

Lines in Supersingular Quartics

We show that the number of lines contained in a supersingular quartic surface is 40 or at most 32, if the characteristic of the field equals 2, and it is 112, 58, or at most 52, if the characteristic equals 3. If the quartic is not supersingular, the number of lines is at most 60 in both cases. We also give a complete classification of large configurations of lines.

The shape of spherical quartics

We discuss the problem of interpolating C Hermite data on the sphere (two points with associated first derivative vectors) by spherical rational curves. With the help of the generalized stereographic projection (Dietz et al., 1993), we construct a two– parameter family of spherical quartics solving this problem. We study the shape of these solutions and derive criteria which guarantee solutions...

Quantifier Elimination for Quartics

Concerning quartics, two particular quantifier elimination (QE) problems of historical interests and practical values are studied. We solve the problems by the theory of complete discrimination systems and negative root discriminant sequences for polynomials that provide a method for real (positive/negative) and complex root classification for polynomials. The equivalent quantifier-free formula...

Rational Points on Quartics

Pseudo-Hermiticity in infinite-dimensional Hilbert spaces

In infinite-dimensional Hilbert spaces, the application of the concept of pseudo-Hermiticity to the description of non-Hermitian Hamiltonians with real spectra may lead to difficulties related to the definition of the metric operator. These difficulties are illustrated by examining some examples taken from the recent literature. We present a formulation that avoids such problems. PACS numbers: ...