Semiample bertini theorems over finite fields

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August undefined, 2024

WebDaniel Erman and Melanie Matchett Wood, Semiample Bertini theorems over finite fields: DOI . This paper extends Poonen's theorem by allowing the ample divisor to be replaced with a semiample divisor, at the expense of losing complete independence of the local conditions. Bounding and counting coefficient objects WebJan 1, 2024 · We study the question of finding smooth hyperplane sections to a pencil of hypersurfaces over finite fields. References [1] Asgarli Shamil , Sharp Bertini theorem for …

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WebMar 29, 2002 · Semiample Bertini theorems over finite fields D. Erman, M. Wood Mathematics 2012 We prove a semiample generalization of Poonen's Bertini Theorem … WebSep 24, 2012 · 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 … map of lake simcoe ontario

arXiv:1209.5266v1 [math.AG] 24 Sep 2012

WebBertini theorems over ﬁnite ﬁelds By Bjorn Poonen* Abstract LetXbe a smooth quasiprojective subscheme of Pnof dimensionm ≥0 over F q. Then there exist homogeneous polynomialsfover F qfor which the intersection ofXand the hypersurfacef= 0 is smooth. In fact, the set of suchfhas a positive density, equal toζ X(m+1)−1, whereζ X(s)=Z WebJan 15, 2015 · 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 … WebBERTINI THEOREMS OVER FINITE FIELDS BJORN POONEN Abstract. Let X be a smooth quasiprojective subscheme of Pn of dimension m ≥ 0 over F q. Then there exist homogeneous polynomials f over F q for which the intersection of X and the hypersurface f = 0 is smooth. In fact, the set of such f has a positive density, equal to ζ X(m + 1)−1, where ... map of lakes in nc mountains

Smoothness of fibers over finite fields - MathOverflow

WebFor a smooth projective variety over a finite field, Poonen’s Bertini Theorem computes the probability that a high degree hypersurface section of that variety will be smooth. We prove a semiample generalization of Poonen's result, where the probability of smoothness is computed as a product of local probabilities taken over the ﬁbers of a ... Webtion \assume that the ground eld kis in nite" from other theorems in the literature. 2. Bertini over finite fields: the closed point sieve Sections 2.1, 2.2, and 2.3 are devoted to the … map of lake sinaiWebstructural and combinatorial results for varieties over finite fields. In this thesis we will discuss three results which come, in part, as a consequence of this technique. First we will discuss semiample Bertini Theorems over finite fields, wherein we examine the probability with which a semiample complete intersection is smooth. kroger solid white albacore tuna

"WebJan 19, 2024 · (i) As the base field is algebraically closed, the product of curves is a variety; (ii) For more results of Bertini type, we refer Tag 0FD4 and Arxiv 1912.09076. $\blacksquare$ Section 10.4. An Enumerative Problem. Step 1. " - Semiample bertini theorems over finite fields

Semiample bertini theorems over finite fields

WebThis paper investigates the density of hypersurfaces in a projective normal simplicial toric variety over a finite field having a quasismooth intersection with a given quasismooth subscheme. The result generalizes the formula found by … http://www-math.mit.edu/%7Epoonen/papers/bertini.pdf

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WebDOI: 10.1016/J.JPAA.2016.05.027 Corpus ID: 119638824; Random hypersurfaces and embedding curves in surfaces over finite fields @article{Gunther2015RandomHA, title={Random hypersurfaces and embedding curves in surfaces over finite fields}, author={Joseph Gunther}, journal={arXiv: Number Theory}, year={2015} } http://www.numdam.org/articles/10.5802/jtnb.979/

WebBERTINI THEOREMS OVER FINITE FIELDS BJORN POONEN Abstract. Let Xbe a smooth quasiprojective subscheme of Pnof dimension m 0 over F q. Then there exist … WebAbstract We obtain lower bounds for the asymptotic number of rational points of smooth algebraic curves over finite fields. To do this we construct infinite Hilbert class field towers with good parameters. In this way we improve bounds of …

WebIn mathematics, the theorem of Bertini is an existence and genericity theorem for smooth connected hyperplane sections for smooth projective varieties over algebraically closed … WebDec 2, 2014 · 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.

WebJan 15, 2015 · Semiample Bertini theorems over finite fields Daniel Erman, Melanie Matchett Wood Duke Math. J. 164 (1), 1-38, (15 January 2015) DOI: 10.1215/00127094 … map of lakes in maineWebBERTINI THEOREMS OVER FINITE FIELDS 1101 H f ∩ X amounts to m + 1 linear conditions on the Taylor coeﬃcients of a dehomogenization of f at P, and these linear conditions … krogers on 10th shadelandWebWe 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 … map of lakes in canadaWebSemiample Bertini theorems over finite fields, with Daniel Erman, Duke Mathematical Journal 164 (2015), no. 1, 1-38. old arxiv preprint. This paper gives the probability that a section of nA+dE is smooth, where A and E are a very ample and globally generated (respectively) divisor on a fixed variety over a finite field, as d goes to infinity. map of lake sinclair eatonton gaWebKEYWORDS: Bertini problems, Grothendieck ring of varieties, motivic probability, radicial surjective morphisms, 14G10, 55R80 Read Abstract + We formulate and prove an analog of Poonen’s finite-field Bertini theorem with Taylor conditions that holds in the Grothendieck ring of varieties. map of lake sinclair georgiaWebFeb 7, 2024 · These results are about Bertini theorems for hypersurfaces in a variety. This can be proved using the smoothness theorem fibers of a morphism, but isn't the same … map of lakes in northern indianaWebBERTINI THEOREMS OVER FINITE FIELDS BJORN POONEN Abstract. Let Xbe a smooth quasiprojective subscheme of Pnof dimension m 0 over F q. Then there exist homogeneous polynomials fover F qfor which the intersection of X and the hypersurface f = 0 is smooth. In fact, the set of such f has a positive density, equal to X(m+ 1)1, where X(s) = Z map of lakes in new hampshire