Genus two reduced quasi-map invariants for CY3 complete intersections
In joint work with Jeongseok Oh and M.-L. Li, we define genus two reduced quasi-map invariants for Calabi-Yau 3-folds embedded in projective space or product of complete intersections, and study standard versus reduced formula as an analogue of the genus 1 case proved by Zinger.
For the definition of reduced invariants and proof of the formula, we use desingularization of genus two quasi-map space, which is a simple analogue of the desingularization of the genus two stable map space constructed by Hu-Li-Niu.
We describe this desingularization and its local chart, local equation explicitly and using this, we explain how we can split virtual cycle to a reduced part (on main component) and boundary part. If time is allowed, I will also explain how we can compute boundary virtual cycle to obtain the formula.