K ¨ Ahler Reductions, K ¨ Ahler Cuts and Coisotropic Actions
نویسنده
چکیده
Let M be a Kähler compact manifold and let G be a subgroup of its full isometry group. Assume G acts in a Hamilton-ian fashion and that it has a one-dimensional center. In this article we analyze the Kähler reduction M λ and the Kähler cut M λ with respect to the Hamiltonian action of the center Z(G). We prove among other results if K is a compact Lie subgroup of K s , where K s is the semisimple connected Lie subgroup of G, whose Lie algebra is [g, g], then K acts coisotropically on M if and only if it acts coisotropically on M λ and K acts cosiotropically on M λ if and only if Z(G) · K acts coisotropically on M. We apply these results to P n (C), the blow up of P 2 (C) at three points and finally to the blow up of P n (C) at one point.
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