Duke Mathematical Journal

Standard conjectures for the arithmetic Grassmannian G(2,N) and Racah polynomials

Andrew Kresch and Harry Tamvakis

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We prove the arithmetic Hodge index and hard Lefschetz conjectures for the Grassmannian G(2,N) parametrizing lines in projective space, for the natural arithmetic Lefschetz operator defined via the Plücker embedding of G in projective space. The analysis of the Hodge index inequality involves estimates on values of certain Racah polynomials.

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Duke Math. J., Volume 110, Number 2 (2001), 359-376.

First available in Project Euclid: 18 June 2004

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Zentralblatt MATH identifier

Primary: 14G40: Arithmetic varieties and schemes; Arakelov theory; heights [See also 11G50, 37P30]
Secondary: 14C17: Intersection theory, characteristic classes, intersection multiplicities [See also 13H15] 14M15: Grassmannians, Schubert varieties, flag manifolds [See also 32M10, 51M35] 33C45: Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) [See also 42C05 for general orthogonal polynomials and functions]


Kresch, Andrew; Tamvakis, Harry. Standard conjectures for the arithmetic Grassmannian G (2, N ) and Racah polynomials. Duke Math. J. 110 (2001), no. 2, 359--376. doi:10.1215/S0012-7094-01-11027-2. https://projecteuclid.org/euclid.dmj/1087574861

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