Arakelov theory of even orthogonal Grassmannians | Zendy

Harry Tamvakis | Zendy

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Arakelov theory of even orthogonal Grassmannians

Author(s) -

Harry Tamvakis

Publication year - 2007

Publication title -

commentarii mathematici helvetici

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.603

H-Index - 46

eISSN - 1420-8946

pISSN - 0010-2571

DOI - 10.4171/cmh/99

Subject(s) - mathematics , intersection theory , pure mathematics , cohomology , linear subspace , cohomology ring , embedding , invariant (physics) , ring (chemistry) , projective space , sesquilinear form , complete intersection , hermitian matrix , moduli space , algebra over a field , mathematical analysis , equivariant cohomology , projective test , differential algebraic equation , ordinary differential equation , chemistry , organic chemistry , artificial intelligence , computer science , mathematical physics , differential equation

We study the Arakelov intersection ring of the arithmetic scheme OG which parametrizes maximal isotropic subspaces in an even dimensional vector space, equipped with the standard hyperbolic quadratic form. We give a presentation of the ring CH(OG) (when OG(C) is given its natural invariant hermitian metric) and formulate an ?arithmetic Schubert calculus? which extends the classical one for the cohomology ring of OG. Our analysis leads to a computation of the Faltings height of OG with respect to its fundamental embedding in projective space, and a comparison of the resulting formula with previous ones, due to Kaiser and Kohler [KK] and the author [T3], [T4].

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