Gluing stability conditions

Hirzebruch面上稳定性条件空间中的墙结构

Wall in the stability space of the gluing stability conditions on Hirzebruch surfaces

本文研究Hirzebruch面上稳定性条件空间的墙结构，通过粘合构造分析几何室与墙的交集，并确定半稳定对象的模空间。

粘合阿贝尔范畴与稳定性条件

Gluing abelian categories and stability conditions

该研究通过双模粘合阿贝尔范畴，证明粘合半稳定对象存在相位间隙时的支撑性质，结合Collins--Polishchuk相位界，还在dg-逗号范畴构造稳定性条件并分析其在半正交分解突变下的行为。

On a deformation of gluing stability conditions

On a triangulated category $\mathbf D$ equipped with a semiorthogonal decomposition $\mathbf D=\langle{\mathbf D_{1}},{\mathbf D_{2}}\rangle$, Collins and Polishchuk develop a gluing construction of stability condition on $\mathbf D$. The gluing construction gives a stability condition on $\mathbf D$ from these on $\mathbf D_{1}$ and $\mathbf D_{2}$. We study a deformation of gluing stability conditions on for a nice semiorthogonal decomposition. As a consequence, we construct a continuous family of stability conditions by showing a deformation property introduced by Bridgeland's original pape…

Explicit Description of A Certain Destabilizing Wall of Skyscraper Sheaves on Ruled Surfaces

We give a explicit description of gluing stability conditions on ruled surfaces by introducing gluing perversity. Moreover, we describe a destabilizing wall of skyscraper sheaves on ruled surfaces by deformation of stability conditions glued from $\widetilde{GL^{+}}(2,\mathbb{R})$-translates of the standard stability condition on the base curve.

Constructing colimits by gluing vector bundles

As already observed by Gabriel, coherent sheaves on schemes obtained by gluing affine open subsets can be described by a simple gluing construction. An example due to Ferrand shows that this fails in general for pushouts along closed immersions, though the gluing construction still works for flat coherent sheaves. We show that by further restricting this gluing construction to vector bundles, we can construct pushouts along arbitrary morphisms (and more general colimits) of certain algebraic stacks called Adams stacks. The proof of this fact uses generalized Tannaka duality and a variant of De…

Quasi-algebraic geometry of curves I. Riemann-Roch theorem and Jacobian

We discuss an analogue of Riemann-Roch theorem for curves with an infinite number of handles. We represent such a curve X by its Shottki model, which is an open subset U of CP^{1} with infinite union of circles as a boundary. An appropriate bundle on X is ω^{1/2} \otimes L, L being a bundle with (say) constants as gluing conditions on the circles. An admissible section of an appropriate bundle on X is a holomorphic half-form on U with given gluing conditions and H^{1/2}-smoothness condition. We study the restrictions on the mutual position of the circles and the gluing constants which guarante…