Morphisms with Only Mild Singular Fibers and Bertini Theorems over Finite Fields

dc.contributor.advisor	Schoen, Chadmark L
dc.contributor.author	Yang, Ziquan
dc.date.accessioned	2016-05-04T16:07:36Z
dc.date.available	2016-05-04T16:07:36Z
dc.date.issued	2016-05-04
dc.department	Mathematics
dc.description.abstract	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 .
dc.identifier.uri	https://hdl.handle.net/10161/11972
dc.language.iso	en_US
dc.subject	Bertini Theorems
dc.subject	Finite Fields
dc.subject	Singular Fibers
dc.subject	Simple Ramification
dc.subject	Elliptic Surfaces
dc.subject	Plane Cubics
dc.title	Morphisms with Only Mild Singular Fibers and Bertini Theorems over Finite Fields
dc.type	Honors thesis

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