An effective Bertini theorem over finite fields
Advances in Geometry · 2003
Let p be a prime, q a power of p and K the algebraic closure of the finite field GFð pÞ. Let X H P N ðKÞ be an irreducible variety. Set n :¼ dimðX Þ and d :¼ degðX Þ. Here we prove that if qd dðd � 1Þ n there is a hyperplane H of P N ðKÞ defined over GFðqÞ and transversal to X. 2000 Mathematics Subject Classification. 14N05