Moscow Mathematical Journal
Volume 15, Issue 2, April–June 2015 pp. 353–372.
Chiral de Rham Complex over Locally Complete Intersections
Given a locally complete intersection X ↪ Y we define a
version of a derived chiral De Rham complex, thereby “chiralizing” a
result by Illusie and Bhatt. A similar construction attaches to a graded
ring a dg vertex algebra, which we prove to be Morita equivalent to a
dg algebra of differential operators. For example, the dg vertex algebra
associated to a fat point, which also arises in the Landau–Ginzburg
model, is shown to be derived rational.
Authors:
Fyodor Malikov (1) and Vadim Schechtman (2)
Author institution:(1) Department of Mathematics, University of Southern California, Los Angeles, CA 90089, USA
(2) Institut de Mathématiques de Toulouse, Université Paul Sabatier, 31062 Toulouse, France
Summary:
Keywords: Vertex algebra, chiral differential operator, dga resolution.
Contents Full-Text PDF