Hermitian metrics, (n-1,n-1) forms and Monge–Ampère equations
نویسندگان
چکیده
منابع مشابه
Hermitian Forms, Trace Equations and Application to Codes
We provide a systematic study of sesquilinear hermitian forms and a new proof of the calculus of some exponential sums defined with quadratic her-mitian forms. The computation of the number of solutions of equations such as Tr Ft/Fs (f (x) + v.x) = 0 or Tr Ft/Fs (f (x)) = a allows us to construct codes and to obtain their parameters.
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Here c1(E, h) is the first Chern form of E with respect to a Hermitian metric h. The famous theorem of Donaldson [7, 8] (for algebraic manifolds only) and Uhlenbeck-Yau [24, 25] says that an irreducible vector bundle E → N is ω-stable if and only if it admits a HermitianEinstein metric (i.e. a metric whose curvature, when the 2-form part is contracted with the metric on N , is a constant times ...
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Signatures of quadratic forms over formally real fields have been generalized in [BP2] to hermitian forms over central simple algebras with involution over such fields. This was achieved by means of an application of Morita theory and a reduction to the quadratic form case. A priori, signatures of hermitian forms can only be defined up to sign, i.e., a canonical definition of signature is not p...
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ژورنال
عنوان ژورنال: Journal für die reine und angewandte Mathematik (Crelles Journal)
سال: 2019
ISSN: 1435-5345,0075-4102
DOI: 10.1515/crelle-2017-0017