Let C ⊂ P be an integral projective curve. One defines the speciality index e(C) of C as the maximal integer t such that h(C, ωC(−t)) > 0, where ωC denotes the dualizing sheaf of C. Extending a classical result of Halphen concerning the speciality of a space curve, in the present paper we prove that if C ⊂ P is an integral degree d curve not contained in any surface of degree < s, in any threef...

We prove that integral points can be effectively determined on all but finitely many modular curves, and on all but one modular curve of prime power level.

Some nonlinear dynamical techniques, including state-space reconstruction and correlation integral, are used to analyze the light curve of 3C 273. The result is compared with a chaotic model. The similarities between them suggest that there is a low-dimensional chaotic attractor in the light curve of 3C 273.

Kirsch’s factorization method is a fast inversion technique for visualizing the profile of a scatterer from measurements of the far-field pattern. The mathematical basis of this method is given by the far-field equation, which is a Fredholm integral equation of the first kind in which the data function is a known analytic function and the integral kernel is the measured (and therefore noisy) fa...

The solutions of the slN Knizhnik-Zamolodchikov(KZ) equations at level 0 are studied. We present the integral formula which is obtained as a quasi-classical limit of the integral formula for form factors of the SU(N) invariant Thirring model due to F. Smirnov. A proof is given that those integrals satisfy slN KZ equation of level 0. The relation of the integral formulae with the chiral Szegö ke...

Let C ⊂ S := P1×P1 be an integral curve and ν : X → C its normalization. Set L := ν∗(OS(1, 0)). Here we give numerical conditions which imply that the pair (X,L) is not the pull-back of a pair (Y,R) with Y a smooth curve of genus q > 0 andR ∈ Pic(Y ). Mathematics Subject Classification: 14H50; 14H51

The writhe of a space curve fragment is considered for various boundary conditions. An expression for the writhe as a function of arclength for an arbitrary space curve is obtained. The formula is built on the base of closing the tangent indicatrix with a geodesic. The corresponding closure of a curve in 3-space is explicitly constructed. The addition rule for writhe is formulated. A relationsh...

We study mirror symmetry for orbifold Hurwitz numbers. We show that the Laplace transform of orbifold Hurwitz numbers satisfy a differential recursion, which is then proved to be equivalent to the integral recursion of Eynard and Orantin with spectral curve given by the r-Lambert curve. We argue that the r-Lambert curve also arises in the infinite framing limit of orbifold Gromov-Witten theory ...