arXiv subjects
Publications and source records attributed to Ville Nordstrom.
We prove a conjecture by Belmans, Fu and Krug concerning the Hochschild homology of the symmetric powers of a small dg category $\mathscr{C}$. More precisely, we show that these groups decompose into pieces that only depend on the Hochschild homology of the dg category $\mathscr{C}$.
We prove a decomposition of the Hochschild homology groups of the equivariant dg category $\mathscr{C}^G$ associated to a small dg category $\mathscr{C}$ with direct sums on which a finite group $G$ acts. When the ground field is $\mathbb{C}$ this decomposition is related to a categorical action of $\text{Rep}(G)$ on $\mathscr{C}^G$ and the resulting action of the representation ring $R_\mathbb{C}(G)$ on $HH_\bullet(\mathscr{C}^G)$.
Given a smooth variety $X$ over $\mathbb{C}$, a smooth divisor $i:Y\hookrightarrow X$ and a global function $f$ on $X$ which vanishes on $Y$ and on its critical locus we compute the map induced on Hochschild homology by the pushforward functor $i_*:D^b(Y)\to D^{abs}(MF(X,f))$ in terms of the Hochschild-Kostant-Rosenberg isomorphisms.
We give explicit formulas for ten compatible Poisson brackets on $\mathbb P^5$ found in arXiv:2007.12351.