3,046 research outputs found
On universal Severi varieties of low genus K3 surfaces
We prove the irreducibility of universal Severi varieties parametrizing
irreducible, reduced, nodal hyperplane sections of primitive K3 surfaces of
genus g, with 3 \le g \le 11, g \neq 10.Comment: Some minor mistakes in the introductory paragraph 1.1 corrected. To
appear in Math.
Newton Method on Riemannian Manifolds: Covariant Alpha-Theory
In this paper we study quantitative aspects of Newton method for finding
zeros of mappings f: M_n -> R^n and vector fields X: M_x -> TM_
Adaptative Step Size Selection for Homotopy Methods to Solve Polynomial Equations
Given a C^1 path of systems of homogeneous polynomial equations f_t, t in
[a,b] and an approximation x_a to a zero zeta_a of the initial system f_a, we
show how to adaptively choose the step size for a Newton based homotopy method
so that we approximate the lifted path (f_t,zeta_t) in the space of (problems,
solutions) pairs.
The total number of Newton iterations is bounded in terms of the length of
the lifted path in the condition metric
On the Curvature of the Central Path of Linear Programming Theory
We prove a linear bound on the average total curvature of the central path of
linear programming theory in terms on the number of independent variables of
the primal problem, and independent on the number of constraints.Comment: 24 pages. This is a fully revised version, and the last section of
the paper was rewritten, for clarit
Moduli of curves on Enriques surfaces
We compute the number of moduli of all irreducible components of the moduli
space of smooth curves on Enriques surfaces. In most cases, the moduli maps to
the moduli space of Prym curves are generically injective or dominant.
Exceptional behaviour is related to existence of Enriques--Fano threefolds and
to curves with nodal Prym-canonical model.Comment: Final version, to appear in Advances in Mathematic
- …