Parabolic Sheaves Research Articles

Infinite root stacks and quasi-coherent sheaves on logarithmic schemes

We define and study infinite root stacks of fine and saturated logarithmic schemes, a limit version of the root stacks introduced by Niels Borne and the second author. We show in particular that the infinite root stack determines the logarithmic structure, and recovers the Kummer-flat topos of the logarithmic scheme. We also extend the correspondence between parabolic sheaves and quasi-coherent sheaves on root stacks to this new setting.

Nahm's Equations, Quiver Varieties and Parabolic Sheaves

Nahm's Equations, Quiver Varieties and Parabolic Sheaves

Nahm's Equations, Quiver Varieties and Parabolic Sheaves

We construct an isomorphism between moduli spaces of solutions of Nahm's equations over the circle and framed moduli spaces of locally free parabolic sheaves over \mathbb P^1 \times \mathbb P^1 through chainsaw quiver varieties.

Parabolic sheaves on logarithmic schemes

We show how the natural context for the definition of parabolic sheaves on a scheme is that of logarithmic geometry. The key point is a reformulation of the concept of logarithmic structure in the language of symmetric monoidal categories, which might be of independent interest. Our main result states that parabolic sheaves can be interpreted as quasi-coherent sheaves on certain stacks of roots.

Moduli of Framed Parabolic Sheaves

This paper gives a construction of the moduli space of framed parabolic sheaves on a Riemann surface. This space serves as a universal, master, space for the well known moduli space of parabolic bundles, as well as moduli spaces of vector bundles, which can all be obtained from this space by torus quotients. The construction is given for the structure group SL(N, C), and indeed is adapted to this case. At the end of the paper, an approach is suggested for dealing with the case of arbitrary reductive groups, involving the associated loop group.

Walls for Gieseker semistability and the Mumford-Thaddeus principle for moduli spaces of sheaves over higher dimensional bases

Let X be a projective manifold over \( \Bbb C \). Fix two ample line bundles H0 and H1 on X. It is the aim of this note to study the variation of the moduli spaces of Gieseker semistable sheaves for polarizations lying in the cone spanned by H0 and H1. We attempt a new definition of walls which naturally describes the behaviour of Gieseker semistability. By means of an example, we establish the possibility of non-rational walls which is a substantially new phenomenon compared to the surface case. Using the approach by Ellingsrud and Gottsche via parabolic sheaves, we were able to show that the moduli spaces undergo a sequence of GIT flips while passing a rational wall. We hope that our results will be helpful in the study of the birational geometry of moduli spaces over higher dimensional bases.

Parabolic sheaves on surfaces and affine Lie algebra

Parabolic sheaves on surfaces and affine Lie algebra

Compactification of moduli of parabolic sheaves and moduli of parabolic Higgs sheaves

Compactification of moduli of parabolic sheaves and moduli of parabolic Higgs sheaves

Parabolic sheaves on higher dimensional varieties

Parabolic sheaves on higher dimensional varieties