nLab
derived critical locus

Idea

The refinement of the notion of critical locus from geometry to derived geometry.

The formal duals to derived critical loci are described by BV-BRST formalism.

A formalization of this in cohesive geometry is at cohesive (infinity,1)-topos – infinitesimal cohesion – critical locus.

References

• Kevin Costello, Owen Gwilliam, Factorization algebras in perturbative quantum field theory – Derived critical locus (web)

• Urs Schreiber: derived critical locus Seminar notes, March 2011

• Gabriele Vezzosi, Derived critical loci I - Basics, arxiv/1109.5213

• Tony Pantev, Bertrand Toen, M. Vaquie, G. Vezzosi, Quantization and derived moduli spaces I: shifted symplectic structures, arxiv/1111.3209

• Kevin Costello, Notes on supersymmetric and holomorphic field theories in dimension 2 and 4 (pdf)