Perverse schobers and Orlov equivalences
Naoki Koseki, Genki Ouchi
TL;DR
This paper constructs examples of perverse schobers on the Riemann sphere, categorifying intersection complexes from mirror symmetry for Calabi-Yau hypersurfaces, using Orlov equivalences.
Contribution
It provides explicit constructions of perverse schobers on the Riemann sphere related to mirror symmetry, advancing the categorification of intersection complexes.
Findings
Constructed examples of perverse schobers on the Riemann sphere
Categorified intersection complexes from mirror symmetry
Utilized Orlov equivalences for the construction
Abstract
A perverse schober is a categorification of a perverse sheaf proposed by Kapranov--Schechtman. In this paper, we construct examples of perverse schobers on the Riemann sphere, which categorify the intersection complexes of natural local systems arising from the mirror symmetry for Calabi-Yau hypersurfaces. The Orlov equivalence plays a key role for the construction.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometric Analysis and Curvature Flows · Geometry and complex manifolds