Donaldson-Thomas theory of $[{\mathbb{C}}^2/{\mathbb{Z}}_{n+1}]\times {\mathbb{P}}^1$

Abstract

We study the relative orbifold Donaldson-Thomas theory of $[{\mathbb{C}}^2/{\mathbb{Z}}_{n+1}]\times {\mathbb{P}}^1$. We establish a correspondence between the DT theory relative to 3 fibers to quantum multiplication by divisors in the Hilbert scheme of points on $[{\mathbb{C}}^2/{\mathbb{Z}}_{n+1}]$. This determines the whole theory if a further nondegeneracy condition is assumed. The result can also be viewed as a crepant resolution correspondence to the DT theory of ${\mathcal{A}}_n\times {\mathbb{P}}^1$.

44 pages, 1 figure. Minor changes, Selecta Mathematica New Series (2018)

References in corpus (2)

• Lectures on K-theoretic computations in enumerative geometry
• Relative Orbifold Donaldson-Thomas Theory and the Degeneration Formula

Cited by in corpus (6)

• The Origin of Calabi-Yau Crystals in BPS States Counting
• A Donaldson-Thomas crepant resolution conjecture on Calabi-Yau 4-folds
• An Overview of Crystals and Double Quiver Yangians
• Relative orbifold Pandharipande-Thomas theory and the degeneration formula
• The orbifold DT/PT vertex correspondence
• Gromov--Witten theory of $[{\mathbb{C}}^2/{\mathbb{Z}}_{n+1}]\times {\mathbb{P}}^1$