# Projectivity of the moduli space of stable curves

@inproceedings{Knudsen1976ProjectivityOT, title={Projectivity of the moduli space of stable curves}, author={F. F. Knudsen}, year={1976} }

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## 453 Citations

The Picard group of the compactified universal Jacobian

- Mathematics
- 2010

We determine explicitly the Picard groups of the universal Jacobian stack and of its compactification over the stack of stable curves. Along the way, we prove some results concerning the gerbe…

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Degenerating Riemann Surfaces and the Quillen Metric

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The degeneration of the Quillen metric for a one-parameter family of Riemann surfaces has been studied by Bismut-Bost and Yoshikawa. In this article, we propose a more geometric point of view using…

Lectures on Stability and Constant Scalar Curvature

- Mathematics
- 2007

An introduction is provided to some current research trends in stability in geometric invariant theory and the problem of Kaehler metrics of constant scalar curvature. Besides classical notions such…

Fundamental groups of moduli stacks of stable curves of compact type

- Mathematics
- 2009

Mg;n , for 2g 2Cn> 0, be the moduli stack of n‐pointed, genus g , stable complex curves of compact type. Various characterizations and properties are obtained of both the topological and algebraic…

Applications of the moduli continuity method to log K‐stable pairs

- MathematicsJournal of the London Mathematical Society
- 2020

The ‘moduli continuity method’ permits an explicit algebraisation of the Gromov–Hausdorff compactification of Kähler–Einstein metrics on Fano manifolds in some fundamental examples. In this paper, we…

RECURSIVE COMBINATORIAL ASPECTS OF COMPACTIFIED MODULI

- Mathematics
- 2018

In recent years an interesting connection has been established between some moduli spaces of algebro-geometric objects (e.g. algebraic stable curves) and somemoduli spaces of polyhedral objects (e.g.…

Coupled vortex equations and moduli: deformation theoretic approach and Kähler geometry

- Mathematics
- 2008

We investigate differential geometric aspects of moduli spaces parametrizing solutions of coupled vortex equations over a compact Kähler manifold X. These solutions are known to be related to…

Generalized Hitchin systems on rational surfaces

- Mathematics
- 2013

By analogy with work of Hitchin on integrable systems, we construct natural relaxations of several kinds of moduli spaces of difference equations, with special attention to a particular class of…

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- Mathematics
- 2018

We study the fixed loci for the action of tensorisation by a line bundle of order $n$ on the moduli space of Higgs bundles for the Langlands self-dual group $\mathrm{GL}(n,\mathbb{C})$. We equip…