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Article Dans Une Revue Mathematische Zeitschrift Année : 2016

Quantization of Donaldson's heat flow over projective manifolds

Résumé

Consider $E$ a holomorphic vector bundle over a projective manifold $X$ polarized by an ample line bundle $L$. Fix $k$ large enough, the holomorphic sections $H^0(E\otimes L^k)$ provide embeddings of $X$ in a Grassmanian space. We define the \textit{balancing flow for bundles} as a flow on the space of projectively equivalent embeddings of $X$. This flow can be seen as a flow of algebraic type hermitian metrics on $E$. At the quantum limit $k\to \infty$, we prove the convergence of the balancing flow towards the Donaldson heat flow, up to a conformal change. As a by-product, we obtain a numerical scheme to approximate the Yang-Mills flow in that context.

Dates et versions

hal-01282371 , version 1 (03-03-2016)

Identifiants

Citer

Julien Keller, Reza Seyyedali. Quantization of Donaldson's heat flow over projective manifolds. Mathematische Zeitschrift, 2016, 282 (3), pp.839-866. ⟨10.1007/s00209-015-1567-8⟩. ⟨hal-01282371⟩
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