Parabolic sheaves on logarithmic schemes

Abstract

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.

37 pages

References in corpus (2)

• Kobayashi-Hitchin correspondence for tame harmonic bundles and an application
• Fibrés paraboliques et champ des racines

Cited by in corpus (28)

• Orbifold techniques in degeneration formulas
• Infinite root stacks and quasi-coherent sheaves on logarithmic schemes
• Toric Stacks I: The Theory of Stacky Fans
• Gromov-Witten theory with maximal contacts
• Kato-Nakayama spaces, infinite root stacks, and the profinite homotopy type of log schemes
• Semistable reduction in characteristic 0
• A smooth compactification of the space of genus two curves in projective space via logarithmic geometry and Gorenstein curves
• Pixton's formula and Abel-Jacobi theory on the Picard stack
• Universal Weak Semistable Reduction
• The degeneration formula for logarithmic expanded degenerations
• Tangent curves to degenerating hypersurfaces
• Holonomic and perverse logarithmic D-modules
• On a logarithmic version of the derived McKay correspondence
• Betti realization of varieties defined by formal Laurent series
• Logarithmic moduli of roots of line bundles on curves
• The circle quantum group and the infinite root stack of a curve (with an appendix by Tatsuki Kuwagaki)
• A general formalism for logarithmic structures
• Gluing semi-orthogonal decompositions
• G-theory of root stacks and equivariant K-theory
• Categorical Logarithmic Hodge Theory, I
• On the essential (p)-dimension of parabolic bundles on a curve
• Smoothability of relative stable maps to stacky curves
• Moduli of parabolic sheaves and filtered Kronecker modules
• Log Fundamental Group Scheme
• Moduli of parabolic sheaves on a polarized logarithmic scheme
• On the Bogomolov-Gieseker inequality for tame Deligne-Mumford surfaces
• Moduli spaces of parabolic bundles over ${\mathbb{P}}^1$ with five marked points
• Building Data for Stacky Covers