The categorical wall-crossing formula for DT/PT quivers

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Algebraic Geometry

The categorical wall-crossing formula for DT/PT quivers

The local categorical DT/PT correspondence

We prove the categorical wall-crossing formula for certain quivers containing the three loop quiver, which we call dt/pt quivers.

The resulting formula is a semiorthogonal decomposition which involves quasi-bps categories studied in our previous papers, and we refer to it as a categorical analogue of the numerical dt/pt correspondence.

Authors

Tudor Pădurariu, Yukinobu Toda

Related Topics

Local models

Matrix factorizations

Semiorthogonal decomposition

Dg categories

Fully faithful functor

Dg-categories @ xmath43

Curve counting theories

Dt / pt correspondence

Dg-categories of matrix factorizations

Introduction

We give a categorical wall-crossing formula for certain (twisted) noncommutative resolutions of singularities introduced by špenko and van den bergh @cite1.1.2.

The main result is motivated by our pursuit of categorifying the correspondence for curve counting theories on calabi-yau 3-folds.

We apply it to obtain a categorical (and k-theoretic) correspondence in a geometric example, for sheaves supported on reduced plane curves in the affine three dimensional space.

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