Embeddings of Derived Categories of Moduli Spaces into Symmetric Powers

Source abstract

We give a criterion for the box product of a Fourier--Mukai kernel to induce a fully faithful functor to the derived category of a symmetric quotient stack. This leads to many new examples of embeddings of derived categories of moduli spaces. We study in more detail the case of the moduli space of stable bundles on a curve. Concretely, we identify pieces of the left-orthogonal complement of our embedding, and extend the known semi-orthogonal decomposition of the moduli space of bundles with rank 2 and fixed determinant to the moduli space of bundles with varying determinant.