arXiv subjects
Publications and source records attributed to Uttaran Dutta.
We illustrate the typical usage of Bayer and Macrì's Positivity Lemma to compute the nef cones of the Hilbert schemes $X^{[n]}$ by combining the Bridgeland stability methods (for large $n$) and classical methods (for small $n$). We use Mori dream K3 surfaces $X$ of Picard rank $2$ as our working example. We also compute the nef cones of the nested Hilbert schemes $X^{[n,n+1]}$ for such $X$, for large $n$.
This work studies conditions under which integral transforms induce exact functors on singularity categories between schemes that are proper over a Noetherian base scheme. A complete characterization for this behavior is provided, which extends earlier work of Ballard and Rizzardo. We leverage a description of the bounded derived category of coherent sheaves as finite cohomological functors on the category of perfect complexes, which is an application of Neeman's approximable triangulated categories, to reduce arguments to an affine local setting. Moreover, we study adjoints of such functors, extend a result of Olander to varieties with mild singularities, and provide an obstruction for derived equivalences between singular varieties.