On the classification of non-normal cubic hypersurfaces
نویسندگان
چکیده
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on the effect of linear & non-linear texts on students comprehension and recalling
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15 صفحه اولIntegral Points on Cubic Hypersurfaces
Let g ∈ Z[x1, . . . , xn] be an absolutely irreducible cubic polynomial whose homogeneous part is non-degenerate. The primary goal of this paper is to investigate the set of integer solutions to the equation g = 0. Specifically, we shall try to determine conditions on g under which we can show that there are infinitely many solutions. An obvious necessary condition for the existence of integer ...
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A remarkable result of [Segre43] says that a smooth cubic surface over Q is unirational iff it has a rational point. [Manin72, II.2] observed that similar arguments work for higher dimensional cubic hypersurfaces satisfying a certain genericity assumption over any infinite field. [CT-S-SD87, 2.3.1] extended the result of Segre to any normal cubic hypersurface (other than cones) over a field of ...
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In this paper, we give a Prym-Tjurin construction for the cohomology and the Chow groups of a cubic hypersurface. On the space of lines meeting a given rational curve, there is the incidence correspondence. This correspondence induces an action on the primitive cohomology and the primitive Chow groups. We first show that this action satisfies a quadratic equation. Then the Abel-Jacobi mapping i...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2011
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2010.12.007