Categorical Donaldson-Thomas theory for local surfaces: $\mathbb{Z}/2$-periodic version

Abstract

We prove two kinds of $\mathbb{Z}/2$-periodic Koszul duality equivalences for triangulated categories of matrix factorizations associated with $(-1)$-shifted cotangents over quasi-smooth affine derived schemes. We use this result to define $\mathbb{Z}/2$-periodic version of Donaldson-Thomas categories for local surfaces, whose ${\mathbb{C}}^{\ast }$-equivariant version was introduced and developed in the author's previous paper. We compare $\mathbb{Z}/2$-periodic DT category with the ${\mathbb{C}}^{\ast }$-equivariant one, and deduce wall-crossing equivalences of $\mathbb{Z}/2$-periodic DT categories from those of ${\mathbb{C}}^{\ast }$-equivariant DT categories.

26 pages. arXiv admin note: text overlap with arXiv:1907.09076

References in corpus (3)

• Higher Topos Theory
• K-theory and the singularity category of quotient singularities
• Birational geometry for d-critical loci and wall-crossing in Calabi-Yau 3-folds