The probability that a complete intersection is smooth

Alina Bucur; Kiran S. Kedlaya

Displaying similar documents to “The probability that a complete intersection is smooth”

Formulae for the singularities at infinity of plane algebraic curves.

Gwoździewicz, Janusz, Płoski, Arkadiusz (2001)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

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Non-zero constant Jacobian polynomial maps of $ℂ ²$

Nguyen Van Chau (1999)

Annales Polonici Mathematici

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We study the behavior at infinity of non-zero constant Jacobian polynomial maps f = (P,Q) in ℂ² by analyzing the influence of the Jacobian condition on the structure of Newton-Puiseux expansions of branches at infinity of level sets of the components. One of the results obtained states that the Jacobian conjecture in ℂ² is true if the Jacobian condition ensures that the restriction of Q to the curve P = 0 has only one pole.

Residual representation of algebraic-geometric codes.

Hübl, Reinhold (2001)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

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Computation of 2-groups of positive classes of exceptional number fields

Jean-François Jaulent, Sebastian Pauli, Michael E. Pohst, Florence Soriano–Gafiuk (2008)

Journal de Théorie des Nombres de Bordeaux

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We present an algorithm for computing the 2-group ${𝒞 ℓ}_{F}^{p o s}$ of the positive divisor classes in case the number field $F$ has exceptional dyadic places. As an application, we compute the 2-rank of the wild kernel $W K_{2} (F)$ in $K_{2} (F)$ .

Isolated intersection multiplicity and regular separation of analytic sets

Piotr Tworzewski (1993)

Annales Polonici Mathematici

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An isolated point of intersection of two analytic sets is considered. We give a sharp estimate of their regular separation exponent in terms of intersection multiplicity and local degrees.

Approximation exponents for algebraic functions in positive characteristic

Bernard de Mathan (1992)

Acta Arithmetica

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In this paper, we study rational approximations for algebraic functions in characteristic p > 0. We obtain results for elements satisfying an equation of the type $α = (A α^{q} + B) / (C α^{q} + D)$ , where q is a power of p.

Growth at infinity of a polynomial with a compact zero set

Janusz Gwoździewicz (1998)

Banach Center Publications

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The fluctuations in the number of points on a family of curves over a finite field

Maosheng Xiong (2010)

Journal de Théorie des Nombres de Bordeaux

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Let $l \geq 2$ be a positive integer, $𝔽_{q}$ a finite field of cardinality $q$ with $q \equiv 1 (mod l)$ . In this paper, inspired by [, , ] and using a slightly different method, we study the fluctuations in the number of $𝔽_{q}$ -points on the curve $ℂ_{F}$ given by the affine model $ℂ_{F} : Y^{l} = F (X)$ , where $F$ is drawn at random uniformly from the set of all monic $l$ -th power-free polynomials $F \in 𝔽_{q} [X]$ of degree $d$ as $d \to \infty$ . The method also enables us to study the fluctuations in the number of $𝔽_{q}$ -points on the same family of curves arising from the set of monic...

Small generators of function fields

Martin Widmer (2010)

Journal de Théorie des Nombres de Bordeaux

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Let $𝕂 / k$ be a finite extension of a global field. Such an extension can be generated over $k$ by a single element. The aim of this article is to prove the existence of a ”small” generator in the function field case. This answers the function field version of a question of Ruppert on small generators of number fields.