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Heat flows for extremal Kähler metrics

Santiago R. Simanca — 2005

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Let ( M , J , Ω ) be a closed polarized complex manifold of Kähler type. Let G be the maximal compact subgroup of the automorphism group of ( M , J ) . On the space of Kähler metrics that are invariant under G and represent the cohomology class Ω , we define a flow equation whose critical points are the extremal metrics,those that minimize the square of the L 2 -norm of the scalar curvature. We prove that the dynamical system in this space of metrics defined by the said flow does not have periodic orbits, and that its only...

Codimension two transcendental submanifolds of projective space

Wojciech KucharzSantiago R. Simanca — 2010

Annales de l’institut Fourier

We provide a simple characterization of codimension two submanifolds of n ( ) that are of algebraic type, and use this criterion to provide examples of transcendental submanifolds when n 6 . If the codimension two submanifold is a nonsingular algebraic subset of n ( ) whose Zariski closure in n ( ) is a nonsingular complex algebraic set, then it must be an algebraic complete intersection in n ( ) .

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