Stability of Tangent Bundles and Tevelev Degrees of Hirzebruch Surfaces

In this talk, I will explain how the non-vanishing of certain curve counts, known as Tevelev degrees, implies the stability of the tangent bundle TX​ with respect to a specified curve class. I will then apply this result to establish the vanishing of most of Tevelev degrees for Hirzebruch surfaces and compute the remaining cases by relating them to the corresponding invariants of the projective line. This is joint work with Carl Lian.