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

Momentum maps and the K\"ahler property for base spaces of reductive principal bundles

We investigate the complex geometry of total spaces of reductive principal bundles over compact base spaces and establish a close relation between the K\"ahler property of the base, momentum maps for the action of a maximal compact subgroup on the total space, and the K\"ahler property of special equivariant compactifications. We provide many examples illustrating that the main result is optimal.Comment: 10 page

Hamiltonian actions of unipotent groups on compact K\"ahler manifolds

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.Comment: v2: 30 pages, final version as accepted by EPIG

Partially ample line bundles on toric varieties

In this note we study properties of partially ample line bundles on simplicial projective toric varieties. We prove that the cone of q-ample line bundles is a union of rational polyhedral cones, and calculate these cones in examples. We prove a restriction theorem for big q-ample line bundles, and deduce that q-ampleness of the anticanonical bundle is not invariant under flips. Finally we prove a Kodaira-type vanishing theorem for q-ample line bundles.Comment: 12 pages, 2 figures; v.2: proofs simplified, lots of material added, new autho

Advanced laser-plasma diagnostics for a modular high-repetition-rate plasma electron accelerator

We present a laser–plasma electron accelerator module designed to be driven by high-repetition-rate lasers for industrial applications of laser-driven electron beams. It consists of a single vacuum chamber containing all the necessary components for producing, optimizing, and monitoring electron beams generated via laser wakefield acceleration in a gas jet when driven by a suitable laser. The core methods in this paper involve a comprehensive metrological assessment of the driving laser by rigorous temporal laser pulse characterization and contrast measurements, supplemented by detailed spatiotemporal distribution analyses of the laser focus. Results demonstrate the good stability and reproducibility of the laser system, confirming its suitability for advanced scientific and industrial applications. We further demonstrate the functionality of the laser–plasma accelerator module diagnostics, perform target density characterizations, and time-resolved laser–plasma shadowgraphy. Current limitations of the set-up preventing first electron acceleration are analyzed and an outlook for future experiments is given. Our work is a first step towards the wide dissemination of fully integrated laser–plasma accelerator technology

Highly Selective PTK2 Proteolysis Targeting Chimeras to Probe Focal Adhesion Kinase Scaffolding Functions

Focal adhesion tyrosine kinase (PTK2) is often overexpressed in human hepatocellular carcinoma (HCC), and several reports have linked PTK2 depletion and/or pharmacological inhibition to reduced tumorigenicity. However, the clinical relevance of targeting PTK2 still remains to be proven. Here, we present two highly selective and functional PTK2 proteolysis-targeting chimeras utilizing von Hippel–Lindau and cereblon ligands to hijack E3 ligases for PTK2 degradation. BI-3663 (cereblon-based) degrades PTK2 with a median DC₅₀ of 30 nM to >80% across a panel of 11 HCC cell lines. Despite effective PTK2 degradation, these compounds did not phenocopy the reported antiproliferative effects of PTK2 depletion in any of the cell lines tested. By disclosing these compounds, we hope to provide valuable tools for the study of PTK2 degradation across different biological systems