Formality of $\mathbb{P}$-objects

Abstract

We show that a $\mathbb{P}$-object and simple configurations of $\mathbb{P}$-objects have a formal derived endomorphism algebra. Hence the triangulated category (classically) generated by such objects is independent of the ambient triangulated category. We also observe that the category generated by the structure sheaf of a smooth projective variety over the complex numbers only depends on its graded cohomology algebra.

23 pages, many changes to improve presentation, strengthened results in Section 5, same content as published version

References in corpus (3)

• Structure of $A(\infty )$-algebra and Hochschild and Harrison cohomology
• Rigid divisors on surfaces
• $\partial \bar{\partial }$-complex symplectic and Calabi-Yau manifolds: Albanese map, deformations and period maps

Cited by in corpus (4)

• Tilting objects in periodic triangulated categories
• Asymmetry of $\mathbb{P}$-Functors
• Relations among $\mathbb{P}$-Twists
• Faithful actions of braid groups by twists along ADE-configurations of spherical objects