Double cubics and double quartics
نویسندگان
چکیده
منابع مشابه
Double Cubics and Double Quartics
In this paper we study a double cover ψ : X → V ⊂ P branched over a smooth divisor S ⊂ V such that n ≥ 7, the degree of V is 3 or 4, and S is cut on the hypersurface V by a hypersurface of degree 2(n− deg(V )). The variety X is rationally connected, because it is a smooth Fano variety. We prove that X is birationally superrigid. In particular, the variety X is nonrational.
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Let K be a field and f(X) be a separable polynomial in K[X]. The Galois group of f(X) over K permutes the roots of f(X) in a splitting field, and labeling the roots as r1, . . . , rn provides an embedding of the Galois group into Sn. We recall without proof two theorems about this embedding. Theorem 1.1. Let f(X) ∈ K[X] be a separable polynomial of degree n. (a) If f(X) is irreducible in K[X] t...
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We construct families of quartic and cubic hypersurfaces through a canonical curve, which are parametrized by an open subset in a Grassmannian and a Flag variety respectively. Using G. Kempf’s cohomological obstruction theory, we show that these families cut out the canonical curve and that the quartics are birational (via a blowing-up of a linear subspace) to quadric bundles over the projectiv...
متن کاملGalois Groups of Cubics and Quartics in All Characteristics
Treatments of Galois groups of cubic and quartic polynomials usually avoid fields of characteristic 2. Here we will discuss these Galois groups and allow all characteristics. Of course, to have a Galois group of a polynomial we will assume our cubic and quartic polynomials are separable, and to avoid reductions to lower degree polynomials we will assume they are irreducible as well. So our sett...
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ژورنال
عنوان ژورنال: Mathematische Zeitschrift
سال: 2006
ISSN: 0025-5874,1432-1823
DOI: 10.1007/s00209-005-0879-5