Hodge Theory on Metric Spaces
نویسندگان
چکیده
منابع مشابه
Hodge Theory on Metric Spaces
Hodge theory is a beautiful synthesis of geometry, topology, and analysis, which has been developed in the setting of Riemannian manifolds. On the other hand, spaces of images, which are important in the mathematical foundations of vision and pattern recognition, do not fit this framework. This motivates us to develop a version of Hodge theory on metric spaces with a probability measure. We bel...
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Recall that a Mumford–Tate domain DM is an open set in its compact dual ĎM — the latter is a rational homogeneous variety defined over Q (think of the upper half plane H ⊂ P1). Thus a polarized Hodge structure (PHS) φ has an “upstairs” field of definition k(φ). If H•,• ⊂ T •,• is a subalgebra then the Noether-Lefschetz locus NLH = {φ : Hg•,• φ ⊇ H} is defined over Q. Its components are defined ...
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ژورنال
عنوان ژورنال: Foundations of Computational Mathematics
سال: 2011
ISSN: 1615-3375,1615-3383
DOI: 10.1007/s10208-011-9107-3