Ranks and symmetric ranks of cubic surfaces
نویسندگان
چکیده
منابع مشابه
On the Ranks and Border Ranks of Symmetric Tensors
Motivated by questions arising in signal processing, computational complexity, and other areas, we study the ranks and border ranks of symmetric tensors using geometric methods. We provide improved lower bounds for the rank of a symmetric tensor (i.e., a homogeneous polynomial) obtained by considering the singularities of the hypersurface defined by the polynomial. We obtain normal forms for po...
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For an elliptic curve over the rationals, Goldfeld’s conjecture [4] asserts that the analytic rank ords=1 L(Ed/Q, s) of quadratic twists Ed of E is positive for squarefree d’s with density 1/2. In other words, the analytic rank of E goes up in quadratic extensions Q( √ d)/Q half of the time. In particular, for every E/Q there are (a) infinitely many quadratic extensions where the rank goes up, ...
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Let M be a compact irreducible Hermitian symmetric space and write M = G/K, with G the group of holomorphic isometries of M and K the stability group of the point of 0 ∈ M . We determine the maximal dimension of a complex projective space embedded in M as a totally geodesic submanifold. AMS Subject Classification: 14L35, 22F30, 20G05 Introduction Let M be a simply connected compact complex mani...
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We introduce various notions of rank for a high order symmetric tensor, namely: rank, border rank, catalecticant rank, generalized rank, scheme length, border scheme length, extension rank and smoothable rank. We analyze the stratification induced by these ranks. The mutual relations between these stratifications, allow us to describe the hierarchy among all the ranks. We show that strict inequ...
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We study the behavior of geometric Picard ranks of K3 surfaces over Q under reduction modulo primes. We compute these ranks for reductions of smooth quartic surfaces modulo all primes p < 2 in several representative examples and investigate the resulting statistics.
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 2020
ISSN: 0747-7171
DOI: 10.1016/j.jsc.2019.10.001