100 research outputs found
Projectivity of analytic Hilbert and Kaehler quotients
We investigate algebraicity properties of quotients of complex spaces by
complex reductive Lie groups G. We obtain a projectivity result for compact
momentum map quotients of algebraic G-varieties. Furthermore, we prove
equivariant versions of Kodaira's Embedding Theorem and Chow's Theorem relative
to an analytic Hilbert quotient. Combining these results we derive an
equivariant algebraisation theorem for complex spaces with projective quotient.Comment: minor changes: title change, typos corrected, obvious issue in the
statement of Thm. 3 fixed, revised proof of Prop. 6.6; 25 pages; to appear in
Transactions of the AM
Partial positivity: geometry and cohomology of q-ample line bundles
We give an overview of partial positivity conditions for line bundles, mostly
from a cohomological point of view. Although the current work is to a large
extent of expository nature, we present some minor improvements over the
existing literature and a new result: a Kodaira-type vanishing theorem for
effective q-ample Du Bois divisors and log canonical pairs.Comment: v1: 24 pages; v2: 25 pages, minor changes, accepted for publication
in the Robfest Proceedings in honor of Rob Lazarsfeld's 60th birthday, London
Mathematical Society Lecture Notes Serie
Invariant meromorphic functions on Stein spaces
In this paper we develop fundamental tools and methods to study meromorphic
functions in an equivariant setup. As our main result we construct quotients of
Rosenlicht-type for Stein spaces acted upon holomorphically by
complex-reductive Lie groups and their algebraic subgroups. In particular, we
show that in this setup invariant meromorphic functions separate orbits in
general position. Applications to almost homogeneous spaces and principal orbit
types are given. Furthermore, we use the main result to investigate the
relation between holomorphic and meromorphic invariants for reductive group
actions. As one important step in our proof we obtain a weak equivariant
analogue of Narasimhan's embedding theorem for Stein spaces.Comment: 20 pages, 1 figur
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