Greb, Daniel and Miebach, Christian - Hamiltonian actions of unipotent groups on compact K\"ahler manifolds

epiga:4486 - Épijournal de Géométrie Algébrique, 9 novembre 2018, Volume 2
Hamiltonian actions of unipotent groups on compact K\"ahler manifolds

Auteurs : Greb, Daniel and Miebach, Christian

We study meromorphic actions of unipotent complex Lie groups on compact K\"ahler manifolds using moment map techniques. We introduce natural stability conditions and show that sets of semistable points are Zariski-open and admit geometric quotients that carry compactifiable K\"ahler structures obtained by symplectic reduction. The relation of our complex-analytic theory to the work of Doran--Kirwan regarding the Geometric Invariant Theory of unipotent group actions on projective varieties is discussed in detail.


Source : oai:arXiv.org:1805.02551
Volume : Volume 2
Publié le : 9 novembre 2018
Déposé le : 8 mai 2018
Mots-clés : Mathematics - Complex Variables,Mathematics - Algebraic Geometry,Mathematics - Differential Geometry,32M05, 32M10, 32Q15, 14L24, 14L30, 37J15, 53D20


Versions

Partager