Curve counting invariants around the conifold point

TL;DR

This paper explores the structure of stability conditions and introduces new curve counting invariants on Calabi-Yau 3-folds near the conifold point, linking algebraic geometry with string theory moduli spaces.

Contribution

It constructs novel DT-type invariants for D0-D2-D6 states and analyzes their wall-crossing behavior and relation to Seidel-Thomas twists.

Findings

Space of stability conditions is a universal cover of a neighborhood of the conifold point.

New curve counting invariants are defined and shown to relate to existing theories.

Wall-crossing formulas for these invariants are derived and studied.

Abstract

In this paper, we investigate the space of certain weak stability conditions on the triangulated category of D0-D2-D6 bound states on a smooth projective Calabi-Yau 3-fold. In the case of a quintic 3-fold, the resulting space is interpreted as a universal covering space of an infinitesimal neighborhood of the conifold point in the stringy Kahler moduli space. We then construct the DT type invariants counting semistable objects in our triangulated category, which are new curve counting invariants on a Calabi-Yau 3-fold. We also investigate the wall-crossing formula of our invariants and their interplay with the Seidel-Thomas twist.