Derived algebraic geometry, determinants of perfect complexes, and applications to obstruction theories for maps and complexes

Timo Schürg, Bertrand Toën, Gabriele Vezzosi
2015 Journal für die Reine und Angewandte Mathematik  
AbstractA quasi-smooth derived enhancement of a Deligne–Mumford stack 𝒳 naturally endows 𝒳 with a functorial perfect obstruction theory in the sense of Behrend–Fantechi. We apply this result to moduli of maps and perfect complexes on a smooth complex projective variety.ForWe give two further applications toAn important ingredient of our construction is a
doi:10.1515/crelle-2013-0037 fatcat:k7f5fzzszrcypiiuiv2xbtz7a4