215 research outputs found
Deformation classification of real non-singular cubic threefolds with a marked line
We prove that the space of pairs formed by a real non-singular cubic hypersurface with a real line has 18 connected components and give for them several quite explicit interpretations. The first one relates these components to the orbits of the monodromy action on the set of connected components of the Fano surface formed by real lines on . For another interpretation we associate with each of the 18 components a well defined real deformation class of real non-singular plane quintic curves and show that this deformation class together with the real deformation class of characterizes completely the component
An Introduction to Algebraic Geometry codes
We present an introduction to the theory of algebraic geometry codes.
Starting from evaluation codes and codes from order and weight functions,
special attention is given to one-point codes and, in particular, to the family
of Castle codes
On rationality of the intersection points of a line with a plane quartic
We study the rationality of the intersection points of certain lines and
smooth plane quartics C defined over F_q. For q \geq 127, we prove the
existence of a line such that the intersection points with C are all rational.
Using another approach, we further prove the existence of a tangent line with
the same property as soon as the characteristic of F_q is different from 2 and
q \geq 66^2+1. Finally, we study the probability of the existence of a rational
flex on C and exhibit a curious behavior when the characteristic of F_q is
equal to 3.Comment: 17 pages. Theorem 2 now includes the characteristic 2 case;
Conjecture 1 from the previous version is proved wron
Locally recoverable codes from rational maps
Producción CientÃficaWe give a method to construct Locally Recoverable Error-Correcting codes.
This method is based on the use of rational maps between affine spaces. The recovery of
erasures is carried out by Lagrangian interpolation in general and simply by one addition
in some good cases.Ministerio de EconomÃa, Industria y Competitividad ( grant MTM2015-65764-C3-1-P)Consejo Nacional de Desarrollo CientÃfico y Tecnológico- Brasil (grants 159852/2014-5 / 201584/2015-8
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