BERTINI THEOREMS OVER FINITE FIELDS BJORN POONEN Abstract. Let X be a smooth quasiprojective subscheme of Pn of dimension m ≥ 0 over

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• Projective geometry
• Algebraic geometry
• Differential topology
• Duality
• Projective space
• Ample line bundle
• Degree of a continuous mapping
• Theorem of Bertini
• Inverse function theorem
• Geometry
• Mathematics
• Abstract algebra