Polar varieties, Bertini's theorems and number of points of singular complete intersections over a finite field

DOI10.1016/j.ffa.2014.09.002zbMath1396.11094arXiv1209.4938OpenAlexW1973512713MaRDI QIDQ473082

Antonio Cafure, Melina Privitelli, Guillermo Matera

Publication date: 21 November 2014

Published in: Finite Fields and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1209.4938

zbMATH Keywords

rational pointssingular locuspolar varietiesvarieties over finite fieldsBertini smoothness theoremDeligne estimateHooley-Katz estimatemultihomogeneous Bézout theorem

Mathematics Subject Classification ID

Singularities in algebraic geometry (14B05) Rational points (14G05) Finite ground fields in algebraic geometry (14G15) Projective techniques in algebraic geometry (14N05) Varieties over finite and local fields (11G25)

Related Items

On the value set of small families of polynomials over a finite field, II, Transverse linear subspaces to hypersurfaces over finite fields, On the value set of small families of polynomials over a finite field. I, Explicit estimates for the number of rational points of singular complete intersections over a finite field, Estimates on the number of \(\mathbb{F}_q\)-rational solutions of variants of diagonal equations over finite fields, Symplectic semifield spreads of PG(5, q^t), q even, Factorization patterns on nonlinear families of univariate polynomials over a finite field

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