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THE EQUATIONS FOR THE MODULI SPACE OF n POINTS ON THE LINE
MODULI SPACE n POINTS ON THE LINE
2015/10/14
A central question in invariant theory is that of determining the relations among invariants. Geometric invariant theory quotients come with a natural ample line bundle, and hence often a natural proj...
AN ANALYTIC CONSTRUCTION OF THE DELIGNE-MUMFORD COMPACTIFICATION OF THE MODULI SPACE OF CURVES
ANALYTIC CONSTRUCTION DELIGNE-MUMFORD COMPACTIFICATION MODULI SPACE OF CURVES
2015/8/26
In 1969, P. Deligne and D. Mumford compactified the modulispace of curves Mg,n. Their compactification Mg,n is a projective algebraic variety, and as such, it has an underlying analytic structure. Alt...
THE AFFINE STRATIFICATION NUMBER AND THE MODULI SPACE OF CURVES
AFFINE STRATIFICATION NUMBER MODULI SPACE
2015/7/14
One relevant example (Example 4.9) turns out to be a proper integral variety with no
embeddings in a smooth algebraic space. This one-paragraph construction appears to be
simpler and more elementary...
Polygons in Minkowski three space and parabolic Higgs bundles of rank two on CP^1
Polygons Minkowski space parabolic bundle Higgs field hyperpolygons
2012/6/8
Consider the moduli space of parabolic Higgs bundles (E,\Phi) of rank two on CP^1 such that the underlying holomorphic vector bundle for the parabolic vector bundle E is trivial. It is equipped with t...
Jet bundles on projective space: New examples
Atiyah sequence jet bundle characteristic class generalized Atiyah class
2012/6/6
In previous papers it was shown that the left and right O-module structure of the jet bundles on the projective line differed. In this paper we show that similar statements hold for jet bundles on pro...
A note on the unramified Brauer group of a homogeneous space
Unramified Brauer group homogeneous space linear algebraic group
2012/6/5
We give a new proof of the theorem stating that for any connected linear algebraic group G over an algebraically closed field k of characteristic 0 and for any closed connected subgroup H of G, the un...
Singularities of the moduli space of level curves
Singularities moduli space of level curves Algebraic Geometry
2012/5/1
For a fixed integer l>1, we describe the singular locus of the compactification of the moduli space R_{g,l} of curves of genus g paired with an l-torsion point in their Jacobian. Generalizing previous...
Torelli theorem for the Deligne--Hitchin moduli space, II
Principal bundle Deligne–Hitchin moduli space Higgs bundle vector field
2012/2/29
Let X and X' be compact Riemann surfaces of genus at least three. Let G and G' be nontrivial connected semisimple linear algebraic groups over C. If some components $M_{DH}^d(X,G)$ and $M_{DH}^{d'}(X'...
Gauge Theories on ALE Space and Super Liouville Correlation Functions
Gauge Theories ALE Space Super Liouville Correlation Functions High Energy Physics - Theory
2011/7/22
Abstract: We present a relation between N=2 quiver gauge theories on the ALE space O_{P^1}(-2) and correlators of N=1 super Liouville conformal field theory, providing checks in the case of punctured ...
Approximate Parametrization of Space Algebraic Curves
Approximate Parametrization Space Algebraic Curves Algebraic Geometry
2011/7/8
Abstract: Given a non-rational real space curve and a tolerance $\epsilon>0$, we present an algorithm to approximately parametrize the curve. The algorithm checks whether a planar projection of the sp...
Isomonodromic tau function on the space of admissible covers
Isomonodromic tau function admissible covers
2009/12/19
The isomonodromic tau function of the Fuchsian differential equations associated to Frobenius structures on Hurwitz spaces can be viewed as a section of a line bundle on the space of admissible covers...