# Compactifications of moduli of $G$-bundles and conformal blocks

@inproceedings{Wilson2021CompactificationsOM, title={Compactifications of moduli of \$G\$-bundles and conformal blocks}, author={Avery S. Wilson}, year={2021} }

For a stable curve of genus g ≥ 2 and simple, simply connected group G, we show that sections of determinant of cohomology on the stack of G-bundles extend to the normalization of its closure in the stack of Schmitt’s honest singular G-bundles. We use this to show that the conformal blocks algebra A onMg is finitely generated and that closed fibers of ProjA → Mg can be interpreted as normalized moduli spaces of singular G-bundles.

## References

SHOWING 1-10 OF 43 REFERENCES

Finite generation of the algebra of type A conformal blocks via birational geometry II: higher genus

- MathematicsProceedings of the London Mathematical Society
- 2019

We prove finite generation of the algebra of type A conformal blocks over arbitrary stable curves of any genus. As an application, we construct a flat family of irreducible normal projective…

Conformal blocks and generalized theta functions

- Mathematics
- 1994

LetSUXr be the moduli space of rankr vector bundles with trivial determinant on a Riemann surfaceX. This space carries a natural line bundle, the determinant line bundleL. We describe a canonical…

Degenerations of the moduli spaces of vector bundles on curves I

- Mathematics
- 1995

LetY be a smooth projective curve degenerating to a reducible curveX with two components meeting transversally at one point. We show that the moduli space of vector bundles of rank two and odd…

Degenerations of the moduli spaces of vector bundles on curves II (generalized Gieseker moduli spaces)

- Mathematics
- 1999

LetX0 be a projective curve whose singularity is one ordinary double point. We construct a birational modelG(n, d) of the moduli spaceU(n, d) of stable torsion free sheaves in the case (n, d)= 1,…

Chern classes of conformal blocks

- Mathematics
- 2009

We derive a formula for the Chern classes of the bundles of conformal blocks on \bar{M}_{0,n} associated to simple finite dimensional Lie algebras and explore its consequences in more detail for sl_2…

Singular principal G-bundles on nodal curves

- Mathematics
- 2005

In the present paper, we give for the first time a general construction of compactified moduli spaces for semistable $G$-bundles on an irreducible complex projective curve $X$ with exactly one node,…

Degeneration of SL(n)-bundles on a reducible curve

- Mathematics
- 2001

We constructed a projective moduli space of semistable torsion free sheaves with `fixed determinant' on a reducible curve. When a family of smooth curves degenerates to the reducible curve, our…

A COMPACTIFICATION OVER Mg OF THE UNIVERSAL MODULI SPACE OF SLOPE-SEMISTABLE VECTOR BUNDLES.

- Mathematics
- 1995

0. Introduction 425 1. The quotient construction 428 2. The fiberwise G.I.T. problem 433 3. Cohomology bounds 435 4. Slope-unstable, torsion free sheaves 437 5. Special, torsion bounded sheaves 440…

The Langlands lemma and the Betti numbers of stacks of $G$--bundles on a curve

- Mathematics
- 1995

In this note we show that the Langlands lemma from the theory of Eisenstein series can be used to invert the recursion relation for the Poincar\'e series of the open substack of semi-stable…

Torsors on semistable curves and degenerations

- MathematicsProceedings - Mathematical Sciences
- 2022

In this paper, we answer two long-standing questions on the classification of G -torsors on curves for an almost simple, simply connected algebraic group G over the field of complex numbers. The…