Séance Séminaire

Séminaire Algèbre Géométrie Algébrique Topologie Algébrique

Derived algebraic geometry and obstruction theories - with applications to stable maps to a K3 surface

We will show how a quasi-smooth derived extension of a Deligne-Mumford stack induces a functorial obstruction theory (in the sense of Behrend-Fantechi) on the underlying stack. This, together with the construction of a determinant map for perfect complexes, will be applied to give a global 'reduced' obstruction theory on the stack of stable maps to a K3 surface, thus clarifying and globalizing the original definition due to Okounkov, Maulik and Pandharipande. This is joint work with T. Schurg and B. Toen.