Lefschetz pencils on a certain hypersurface in positive characteristic
Toshiyuki Katsura
TL;DR
This paper constructs specific symmetric configurations of rational points and lines on a hypersurface in projective 3-space over finite fields, and analyzes the structure of a Lefschetz pencil derived from these lines.
Contribution
It introduces new symmetric configurations of points and lines on a hypersurface in positive characteristic and studies the structure of a Lefschetz pencil formed from these lines.
Findings
Constructed symmetric configurations of rational points and lines.
Determined the structure of a Lefschetz pencil on the hypersurface.
Analyzed configurations over Fq and Fq2 fields.
Abstract
We show that on a certain hypersurface in P3 there is a (q3 + q2 + q + 1)q+1-symmetric configuration (resp. a ((q3 + 1)(q2 + 1)q+1, (q3 + 1)(q + 1)q2+1)) -configuration) made up of the rational points over Fq (resp. over Fq2) and the lines over Fq (resp. the lines over Fq2). We also determine the structure of a Lefschetz pencil made by using a line from these lines.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Coding theory and cryptography · Polynomial and algebraic computation