Results 11 to 20 of about 9,215,739 (339)
Experimental Mathematics, 2017 In this paper we will prove that the six-dimensional G\"opel variety in $P^{134}$ is generated by 120 linear, 35 cubic and 35 quartic relations. This result was already obtained in [RS] , but the authors used a statement in [Co] saying that the G\"opel ...
Freitag, Eberhard +1 more
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The Varieties of Agnosticism [PDF]
The Philosophical Quarterly, 2021 AbstractWe provide a framework for understanding agnosticism. The framework accounts for the varieties of agnosticism while vindicating the unity of the phenomenon. This combination of unity and plurality is achieved by taking the varieties of agnosticism to be represented by several agnostic stances, all of which share a common core provided by what ...
Filippo Ferrari, Luca Incurvati
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Secant varieties of Grassmann varieties [PDF]
Proceedings of the American Mathematical Society, 2004 In this paper we discuss the dimensions of the (higher) secant varieties to the Grassmann varieties, embedded via the Plucker embeddings. We use Terracini's Lemma and the duality in the exterior algebra of a finite dimensional vector space to translate the problem into that of finding the dimension of a graded piece of a " fat" ideal in the exterior ...
GIMIGLIANO, ALESSANDRO +2 more
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Varieties with small discriminant variety [PDF]
Transactions of the American Mathematical Society, 2006 Let X be a smooth complex projective variety, let L be an ample and spanned line bundle on X, V C H°(X,L) defining a morphism Φ V : X → P N and let D(X,V) be its discriminant locus, the variety parameterizing the singular elements of |V|. We present two bounds on the dimension of D(X, V) and its main component relying on the geometry of Φ V (X) ⊂ P N .
A. LANTERI, R. MUNOZ
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Osculating Varieties of Veronese Varieties and Their Higher Secant Varieties [PDF]
Canadian Journal of Mathematics, 2007 AbstractWe consider the k-osculating varieties Ok,n.d to the (Veronese) d-uple embeddings of ℙn. We study the dimension of their higher secant varieties via inverse systems (apolarity). By associating certain 0-dimensional schemes Y ⊂ ℙn to and by studying their Hilbert functions, we are able, in several cases, to determine whether those secant ...
BERNARDI, ALESSANDRA +3 more
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, 2021 This is a chapter in an upcoming Handbook of Automata ...
Straubing, Howard, Weil, Pascal
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Nilpotent varieties and metabelian varieties
Turkish Journal of Mathematics, 2022 We deal with varieties of nonassociative algebras having polynomial growth of codimensions. We describe some results obtained in recent years in the class of left nilpotent algebras of index two. Recently the authors established a correspondence between the growth rates for left nilpotent algebras of index two and the growth rates for commutative or ...
Valenti Angela, Mishchenko Sergey
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Journal of High Energy Physics, 2014 The so-called Scattering Equations which govern the kinematics of the scattering of massless particles in arbitrary dimensions have recently been cast into a system of homogeneous polynomials. We study these as affine and projective geometries which we call Scattering Varieties by analyzing such properties as Hilbert series, Euler characteristic and ...
Cyril Matti +3 more
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Secant varieties of toric varieties
Journal of Pure and Applied Algebra, 2007 v1, AMS LaTex, 5 figures, 25 pages; v2, reference added; v3, This is a major rewrite. We have strengthened our main results to include a classification of smooth lattice polytopes P such that Sec X_P does not have the expected dimension. (See Theorems 1.4 and 1.5.) There was also a considerable amount of reorganization, and some expository material was
David A. Cox, Jessica Sidman
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On the secant varieties of tangential varieties
Journal of Pure and Applied Algebra, 2022 Let $X\subset \mathbb{P}^r$ be an integral and non-degenerate variety. Let $ _{a,b}(X)\subseteq \mathbb{P}^r$, $(a,b)\in \mathbb{N}^2$, be the join of $a$ copies of $X$ and $b$ copies of the tangential variety of $X$. Using the classical Alexander-Hirschowitz theorem (case $b=0$) and a recent paper by H. Abo and N.
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