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An effective Bertini theorem over finite fields. (English) Zbl 1070.14524
Summary: Let $$p$$ be a prime, $$q$$ a power of $$p$$ and $$K$$ the algebraic closure of the finite field $$\mathbb{F}_p$$. Let $$X\subset\mathbb{P}^N(K)$$ be an irreducible variety. Set $$n=\dim(X)$$ and $$d=\deg(X)$$. Here we prove that if $$q\geq d(d-1)^n$$ there is a hyperplane $$H$$ of $$\mathbb{P}^N(K)$$ defined over $$\mathbb{F}_q$$ and transversal to $$X$$.

##### MSC:
 14N05 Projective techniques in algebraic geometry 14G15 Finite ground fields in algebraic geometry
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##### References:
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