The Mellin Transform and Spectral Properties of Toric Varieties
نویسندگان
چکیده
منابع مشابه
The Mellin Transform and Spectral Properties of Toric Varieties
In this article we apply results of [W] on the twisted Mellin transform to problems in toric geometry. In particular we use these results to describe the asymptotics of probability densities associated with the monomial eigenstates, z, k ∈ Z, in Bargmann space and prove an “upstairs” version of the spectral density theorem of [BGU]. We also obtain for the z’s, “upstairs” versions of the results...
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We show that Fourier transforms on the Weyl algebras have a geometric counterpart in the framework of toric varieties, namely they induce isomorphisms between twisted rings of differential operators on regular toric varieties, whose fans are related to each other by reflections of one-dimensional cones. The simplest class of examples is provided by the toric varieties related by such reflection...
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The “twisted Mellin transform” is a slightly modified version of the usual classical Mellin transform on L([0,∞)). In this short note we investigate some of its basic properties. From the point of view of combinatorics one of its most interesting properties is that it intertwines the differential operator, df/dx, with its finite difference analogue, ∇f = f(x)−f(x−1). From the point of view of a...
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If X is a smooth projective toric variety of dimension n we give explicit conditions on characters of the torus giving an embedding X →֒ Pr that guarantee dimSecX = 2n+ 1. We also give necessary and sufficient conditions for a general point of SecX to lie on a unique secant line when X is embedded into Pr using a complete linear system. For X of dimension 2 and 3 we give formulas for deg SecX in...
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ژورنال
عنوان ژورنال: Transformation Groups
سال: 2008
ISSN: 1083-4362,1531-586X
DOI: 10.1007/s00031-008-9027-8