TORIC SHEAVES, STABILITY AND FIBRATIONS - Université Bretagne Sud Access content directly
Journal Articles Journal of Pure and Applied Algebra Year : 2024

TORIC SHEAVES, STABILITY AND FIBRATIONS

Abstract

For an equivariant reflexive sheaf over a polarised toric variety, we study slope stability of its reflexive pullback along a toric fibration. Examples of such fibrations include equivariant blow-ups and toric locally trivial fibrations. We show that stability (resp. unstability) is preserved under such pullbacks for so-called adiabatic polarisations. In the strictly semistable situation, under locally freeness assumptions, we provide a necessary and sufficient condition on the graded object to ensure stability of the pulled back sheaf. As applications, we provide various stable perturbations of semistable tangent sheaves, either by changing the polarisation, or by blowing-up a subvariety. Finally, our results apply uniformly in specific flat families and induce injective maps between the associated moduli spaces.
Fichier principal
Vignette du fichier
toricpullbacks.pdf (378.93 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03807884 , version 1 (10-10-2022)
hal-03807884 , version 2 (27-07-2023)

Identifiers

Cite

Achim Napame, Carl Tipler. TORIC SHEAVES, STABILITY AND FIBRATIONS. Journal of Pure and Applied Algebra, 2024, 228 (3), pp.107494. ⟨10.1016/j.jpaa.2023.107494⟩. ⟨hal-03807884v2⟩
134 View
46 Download

Altmetric

Share

Gmail Facebook X LinkedIn More