Tangent Bundles and fixed domain curve counts

par Alessio Cela (Cambridge)

jeudi 20 nov. 2025, 10:30 → 11:30 Europe/Paris

In this talk, I will explain how the non-vanishing of fixed-domain curve counts (Tevelev degrees) in a fixed curve class implies the stability of the tangent bundle TX​ with respect to that class. I will then apply this result to establish the vanishing of most Tevelev degrees for Hirzebruch surfaces and compute the remaining cases by relating them to the corresponding invariants of the projective line. I will also explain how fixed-domain curve counts can be used to determine the splitting type of the restriction of the tangent bundle of certain varieties along a general rational curve.