  Let $X$ be a smooth variety or orbifold and let $Z \subseteq X$ be a complete
intersection defined by a section of a vector bundle $E \to X$. Originally
proposed by Givental, quantum Serre duality refers to a precise relationship
between the Gromov--Witten invariants of $Z$ and those of the dual vector
bundle $E^\vee$. In this paper we prove a quantum Serre duality statement for
quasimap invariants. In shifting focus to quasimaps, we obtain a comparison
which is simpler and which also holds for non-convex complete intersections. By
combining our results with the wall-crossing formula developed by Zhou, we
recover a quantum Serre duality statement in Gromov-Witten theory without
assuming convexity.
