On Complex Supermanifolds with Trivial Canonical Bundle
Josua Groeger

TL;DR
This paper characterizes when a complex supermanifold has a trivial canonical bundle using algebraic methods, and applies this to Calabi-Yau supermanifolds with explicit formulas involving superholonomy and connections.
Contribution
It provides a new algebraic criterion for trivial canonical bundles on supermanifolds and extends the understanding of Calabi-Yau supermanifolds with explicit formulas.
Findings
Algebraic characterization of trivial canonical bundle
Explicit formula for Calabi-Yau supermanifolds
Use of superholonomy and complex integral forms
Abstract
We give an algebraic characterisation for the triviality of the canonical bundle of a complex supermanifold in terms of a certain Batalin-Vilkovisky superalgebra structure. As an application, we study the Calabi-Yau case, in which an explicit formula in terms of the Levi-Civita connection is achieved. Our methods include the use of complex integral forms and the recently developed theory of superholonomy.
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Taxonomy
TopicsGeometry and complex manifolds · Nonlinear Waves and Solitons · Homotopy and Cohomology in Algebraic Topology
