Morphisms with Only Mild Singular Fibers and Bertini Theorems over Finite Fields
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2016-05-04
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We compute the asymptotic density of non-singular hypersurfaces of bidegree (3, d) in P^n×P^1 with only mild singular fibers over P^1 over a finite field F_q for n = 1, 2. When n = 1 and char F_q > 2, this asymptotic density is ζP1(2)^−2. When n = 2 and char F_q > 3, it is bounded below and above by ζP1 (2)^−1 ζP1 (3/2)^−1 and ζP1(2)^−2 .
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Yang, Ziquan (2016). Morphisms with Only Mild Singular Fibers and Bertini Theorems over Finite Fields. Honors thesis, Duke University. Retrieved from https://hdl.handle.net/10161/11972.
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