EVENT DETAILS AND ABSTRACT

Title: Derived Hilbert schemes
Speaker: Professor Mikhail Kapranov, NU
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Special Note:
Abstract:

Usual Hilbert schemes (parametrizing sheaves of ideals in a given scheme) are particular cases of Quot schemes (parametrizing subsheaves in a given coherent sheaf). In addition to the general construction of the derived Quot scheme (discussed earlier) there is a different, more economical dg-thickening existing only for Hilbert schemes. While the derived Quot schemes are suitable for construction of the derived moduli spaces of vector bundles, the derived Hilbert schemes are suitable for construction of derived moduli spaces of (stable) maps etc. Their construction is based on the derived moduli spaces of commutative algebra structures instead of module structures, as for RQuot.