Derived critical loci I  Basics
Abstract
We will quickly explore the derived geometry of zero loci of sections of vector bundles, with particular emphasis on derived critical loci. In particular we will single out many of the derived geometric structures carried by derived critical loci: the homotopy BatalinVilkovisky structure, the action of the 2monoid of the selfintersection of the zero section, and the derived symplectic structure of degree 1, and show how this structure exists, more generally, on derived lagrangian intersections inside a symplectic manifold. These are just applications of a small part of a much larger project  joint with Pantev, Toën and Vaquié  investigating quantization of derived moduli spaces.
 Publication:

arXiv eprints
 Pub Date:
 September 2011
 DOI:
 10.48550/arXiv.1109.5213
 arXiv:
 arXiv:1109.5213
 Bibcode:
 2011arXiv1109.5213V
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Symplectic Geometry
 EPrint:
 Notes