Let M be a compact Kähler manifold equipped with a Hamiltonian action of a compact Lie group G. In [Invent. Math. 67 (1982), no. 3, 515–538], Guillemin and Sternberg showed that there is a geometrically natural isomorphism between the G-invariant quantum Hilbert space over M and the quantum Hilbert space over the symplectic quotient M//G. This map, though, is not in general unitary, even to lea...

Let M be a compact Kähler manifold equipped with a Hamiltonian action of a compact Lie group G. In [Invent. Math. 67 (1982), no. 3, 515–538], Guillemin and Sternberg showed that there is a geometrically natural isomorphism between the G-invariant quantum Hilbert space over M and the quantum Hilbert space over the symplectic quotient M/G. This map, though, is not in general unitary, even to lead...

We study sequences of infinitely near T -points of a smooth family F/Y of geometrically irreducible surfaces. We destinguish a special sort of such sequences, the strict sequences. To each one, we associate an ordered unweighted Enriques diagram. We prove that the various sequences with a given diagram form a functor, and we represent it by a smooth Y -scheme. We equip this scheme with a free a...

We study the null fiber of a moment map related to dual pairs. We construct an equivariant resolution of singularities of the null fiber, and get conormal bundles of closed KC-orbits in the Lagrangian Grassmannian as the categorical quotient. The conormal bundles thus obtained turn out to be a resolution of singularities of the closure of nilpotent KC-orbits, which is a “quotient” of the resolu...

We study the null fiber of a moment map related to dual pairs. We construct an equivariant resolution of singularities of the null fiber, and get conormal bundles of closed KC-orbits in the Lagrangian Grassmannian as the categorical quotient. The conormal bundles thus obtained turn out to be a resolution of singularities of the closure of nilpotent KC-orbits, which is a “quotient” of the resolu...

Recently, Lima and Randrianarivony pointed out the role of the property (β) of Rolewicz in nonlinear quotient problems, and answered a ten-year-old question of Bates, Johnson, Lindenstrauss, Preiss and Schechtman. In the present paper, we prove that the modulus of asymptotic uniform smoothness of the range space of a uniform quotient map can be compared with the modulus of (β) of the domain spa...

In this paper we improve some mapping theorems on א-spaces. For instance we show that an א-space is preserved by a closed and countably bi-quotient map. This is an improvement of Yun Ziqiu’s theorem: an א-space is preserved by a closed and open map.

Douglas D. MOONEY, Thomas A. RICHMOND Western Kentucky University Bowling Green, KY 42101 USA The ideas of quotient maps, quotient spaces, and upper semicontinuous decompositions are extended to the setting of ordered topological spaces. These tools are used to investigate the semilattice of ordered compactifications and to construct ordered compactifications with o-totally disconnected and o-z...