A moduli-theoretic framework for PDEs via D-Hilbert schemes and Spencer stability is introduced, but the advertised refinement of Donaldson-Uhlenbeck-Yau is a restatement of the classical result.
Derived Moduli Spaces of Nonlinear PDEs II: Variational Tricomplex and BV Formalism
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abstract
This paper is the second in a series of works dedicated to studying non-linear partial differential equations via derived geometric methods. We study a natural derived enhancement of the de Rham complex of a non-linear PDE via algebro-geometric techniques and examine its consequences for the functional differential calculus on the space of solutions. Applications to the BV-formalism with and without boundary conditions are discussed.
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The $\mathcal{D}$-Geometric Hilbert Scheme -- Part I: Involutivity and Stability
A moduli-theoretic framework for PDEs via D-Hilbert schemes and Spencer stability is introduced, but the advertised refinement of Donaldson-Uhlenbeck-Yau is a restatement of the classical result.