On the Virasoro constraints for the product space X×C

Source abstract

Let X be a smooth projective variety with [Formula: see text], and let C be a smooth projective curve of genus h. We study the Virasoro constraints for the fiber-degree-zero sector of the Gromov–Witten theory of [Formula: see text]. We prove that, if the full-genus Virasoro constraints hold for X, then the full-genus fiber-degree-zero Virasoro constraints hold for [Formula: see text]. As an application, the full Gromov–Witten theory of [Formula: see text] satisfies the Virasoro constraints through genus [Formula: see text].