59 citations · 172 across the 27 of their papers we have counts for
32 papers
Subspace concentration condition and Bogomolov--Gieseker inequality
Carl Tipler
We provide a necessary condition for integral polytopes to satisfy subspace concentration type inequalities, by mean of a convex geometric interpretation of the Bogomolov--Gieseker…
Decomposition of toric sheaves
Carl Tipler
We show that the abelian category of coherent toric sheaves is generated, as a Serre subcategory, by pushforwards of rank one reflexive sheaves supported on invariant subvarieties.…
Stable toric sheaves. I : Chern classes
Carl Tipler
We reduce Hartshorne's conjecture on indecomposable rank 2 vector bundles in the semistable case to the non-existence of smoothable rank 2 semistable toric sheaves on the projectiv…
Polynomial stability conditions for vector bundles: Positivity, equivariance and blow-ups
Rémi Delloque, Achim Napame, Carlo Scarpa +1
We introduce the notion of P-critical connections for hermitian holomorphic vector bundles over compact balanced manifolds: integrable hermitian connections whose curvature solves…
Foldable fans, cscK surfaces and local K-moduli
Carl Tipler
We study the moduli space of constant scalar curvature Kähler surfaces around the toric ones. To this aim, we introduce the class of foldable surfaces : smooth toric surfaces whose…
Toric sheaves and flips
Andrew Clarke, Achim Napame, Carl Tipler
Any toric flip naturally induces an equivalence between the associated categories of equivariant reflexive sheaves, and we investigate how slope stability behaves through this func…