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• W1974373203 abstract "We prove a semiample generalization of Poonen's Bertini Theorem over a finite field that implies the existence of smooth sections for wide new classes of divisors. The probability of smoothness is computed as a product of local probabilities taken over the fibers of the morphism determined by the relevant divisor. We give several applications including a negative answer to a question of Baker and Poonen by constructing a variety (in fact one of each dimension) which provides a counterexample to Bertini over finite fields in arbitrarily large projective spaces. As another application, we determine the probability of smoothness for curves in Hirzebruch surfaces, and the distribution of points on those smooth curves." @default.
• W1974373203 created "2016-06-24" @default.
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• W1974373203 date "2015-01-15" @default.
• W1974373203 modified "2023-09-26" @default.
• W1974373203 title "Semiample Bertini theorems over finite fields" @default.
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• W1974373203 doi "https://doi.org/10.1215/00127094-2838327" @default.
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