61,737 research outputs found
On a generic symmetry defect hypersurface
We show that symmetry defect hypersurfaces for two generic members of the irreducible algebraic family of n-dimensional smooth irreducible subvarieties in general position in C²ⁿ are homeomorphic and they have homeomorphic sets of singular points. In particular symmetry defect curves for two generic curves in C² of the same degree have the same numer of singular points
On the maximum number of rational points on singular curves over finite fields
We give a construction of singular curves with many rational points over
finite fields. This construction enables us to prove some results on the
maximum number of rational points on an absolutely irreducible projective
algebraic curve defined over Fq of geometric genus g and arithmetic genus
Codes from Jacobian surfaces
This paper is concerned with some Algebraic Geometry codes on Jacobians of
genus 2 curves. We derive a lower bound for the minimum distance of these codes
from an upper "Weil type" bound for the number of rational points on
irreducible (possibly singular or non-absolutely irreducible) curves lying on
an abelian surface over a finite field
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