The Gauss map and a noncompact Riemann-Roch formula for constructible sheaves on semiabelian varieties

DOI10.1215/S0012-7094-00-10417-6zbMath1021.14016arXivmath/9909088OpenAlexW2038981201MaRDI QIDQ1577515

J. Franecki, Mikhail Kapranov

Publication date: 16 November 2000

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9909088

zbMATH Keywords

Euler characteristicGauss mapcharacteristic cycleperverse sheafsemiabelian varietyconstructible sheafGaussian degreenon-compact Riemann-Roch formula

Mathematics Subject Classification ID

Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry (14C17) Riemann-Roch theorems (14C40) Linear algebraic groups over the reals, the complexes, the quaternions (20G20) Analytic theory of abelian varieties; abelian integrals and differentials (14K20)

Related Items (22)

On parabolic restriction of perverse sheaves ⋮ Vanishing theorems for constructible sheaves on abelian varieties over finite fields ⋮ Semicontinuity of Gauss maps and the Schottky problem ⋮ Constructible Sheaf Complexes in Complex Geometry and Applications ⋮ Likelihood Geometry ⋮ Characteristic cycles and the microlocal geometry of the Gauss map, I ⋮ Mellin transformation, propagation, and abelian duality spaces ⋮ The Maximum Likelihood Degree of Mixtures of Independence Models ⋮ Generic vanishing, 1-forms, and topology of Albanese maps ⋮ Logarithmic cotangent bundles, Chern‐Mather classes, and the Huh‐Sturmfels involution conjecture ⋮ On singular generalizations of the Singer–Hopf conjecture ⋮ On Euler characteristic of equivariant sheaves. ⋮ Perverse sheaves on semi-abelian varieties -- a survey of properties and applications ⋮ Log -modules and index theorems ⋮ A note on discrete mixed volume and Hodge-Deligne numbers ⋮ Characteristic cycles and the microlocal geometry of the Gauss map. II ⋮ Perverse sheaves on semi-abelian varieties ⋮ Cubic threefolds, Fano surfaces and the monodromy of the Gauss map ⋮ On the signed Euler characteristic property for subvarieties of abelian varieties ⋮ Bernstein-Sato ideals and hyperplane arrangements ⋮ Vanishing theorems for constructible sheaves on abelian varieties ⋮ Holonomic \(D\)-modules on abelian varieties

Cites Work

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• A characterization of A-discriminantal hypersurfaces in terms of logarithmic Gauss map
• Characteristic varieties and vanishing cycles
• \({\mathfrak G}\)-module, Springer's representations and bivariant Chern classes
• Generalized Euler integrals and \(A\)-hypergeometric functions
• \(\ell\)-adic perverse sheaves over a torus
• Integral points on subvarieties of semiabelian varieties. I

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