G. Martens′ Dimension Theorem for Curves of Odd Gonality

For a smooth projective irreducible algebraic curve C of odd gonality, the maximal possible dimension of the variety of special linear systems W _d ^r (C) is d-3r by a result of M. Coppens et al. Furthermore it is known that if the maximum dimension of W(C) for a curve C of odd gonality is attained then C is of very special type of curves by the recent progress made by G. Martens. The purpose of this paper is to chase an extension of the result of G. Martens; if dim W(C)=d-3r-1 for a curve C of odd gonality for some dg-4 and r1, then C must be either a smooth plane sextic, a pentagonal curve of bounded genus or a smooth plane octic.     

Double covering of curves

Let be a smooth projective algebraic curve of genus and an integer with . For all integers we prove the existence of a double covering with a smooth curve of genus and the existence of a degree morphism that does not factor through . By the Castelnuovo-Severi inequality, the result is sharp (except perhaps the bound ).

     

Space models of degree g+1 of curves of genus g

It is the aim of this note to determine all smooth curves of genus g admitting a birational space model of degree g + 1 whose plane sections define a complete linear series. And we add criteria when there is a smooth such model.     

A remark on the Hilbert scheme of smooth complex space curves

Partially supported by Korea Science & Engineering Foundation. The author is grateful to the Max-Planck-Institut für Mathematik for the support, where a major part of this paper was written during his stay there.     

Superconducting properties of amorphous transition metal alloys

We have co-sputtered amorphous films of several Mo and W-based superconducting alloys. Measurements of T_c, ($\text{d}\text{H}{}_{\mathrm{c2}}\text{d}\text{T}$)_Tc and the normal state resistivity near T_c were made on a number of these alloys. Our results and other data from the literature are studied to examine the correlation between T_c and the dressed density of states at the Fermi level.     

The elastic constants of V2O3 in the insulating phase

The initial slopes of the acoustic phonon dispersion curves in (V_0.98Cr_0.02)₂O₃ have been measured at room temperature in several of the high symmetry directions by inelastic neutron scattering. From these data several sound velocities and four independent elastic constants have been determined. Although the Cr doped specimen is in the insulating phase and pure V₂O₃ is metallic, these results are in good agreement with recent data (1) obtained by ultrasonic measurements on pure V₂O₃.     

Observation of rf-induced dc voltages in sputtered binary superconducting films

We have observed that an rf current of frequency 1–5 MHz, passing through a sputtered binary superconducting film, can induce a dc voltage as large as 1 mV across the film for temperatures near the critical temperature T_C. The largest induced voltage has been observed in films which are microscopically inhomogeneous, such as Mo₆₃C₃₇ films which exhibit columnar microstructure. We suggest that the effect may be due to an inverse ac Josephson effect in a randomly connected series array of many microscopic superconducting weak links that are expected to exist close to T_C.