Formality of derived intersections and the orbifold HKR isomorphism

Author(s)

Arinkin, Dima ^[1] ; Caldararu, Andrei ^[2] ; Hablicsek, Marton ^[2]

Affiliation

^[1] Univ Wisconsin, Dept Math, 480 Lincoln Dr, Madison, WI 53706 - USA

^[2] Univ Penn, Dept Math, David Rittenhouse Lab, 209 S 33rd St, Philadelphia, PA 19104 - USA

• Document type: Journal article
• Source: Journal of Algebra; v. 540, p. 100-120, DEC 15 2019.
• Web of Science Citations: 0

Abstract

We study when the derived intersection of two smooth subvarieties of a smooth variety is formal. As a consequence we obtain a derived base change theorem for non-transversal intersections. We also obtain applications to the study of the derived fixed locus of a finite group action and argue that for a global quotient orbifold the exponential map is an isomorphism between the Lie algebra of the free loop space and the loop space itself. This allows us to give new proofs of the HKR decomposition of orbifold Hochschild (co)homology into twisted sectors. (C) 2019 Published by Elsevier Inc. (AU)

• FAPESP's process: 17/21429-6 - The structure problems of Zinbiel-Lie and Novikov-Jordan algebras
• Grantee: Nurlan Ismailov
• Support Opportunities: Scholarships in Brazil - Post-Doctoral