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Chiral de Rham complex over locally complete intersections
Fyodor Malikova, Vadim Schechtmanb a Department of Mathematics, University of Southern California, Los Angeles, CA 90089, USA
b Institut de Mathématiques de Toulouse, Université Paul Sabatier, 31062 Toulouse, France
Abstract:
Given a locally complete intersection $X\hookrightarrow Y$ 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.
Key words and phrases:
vertex algebra, chiral differential operator, dga resolution.
Received: May 30, 2014
Citation:
Fyodor Malikov, Vadim Schechtman, “Chiral de Rham complex over locally complete intersections”, Mosc. Math. J., 15:2 (2015), 353–372
Linking options:
https://www.mathnet.ru/eng/mmj563 https://www.mathnet.ru/eng/mmj/v15/i2/p353
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