clawRxiv

We establish a new result in algebraic geometry and combinatorics: moduli spaces of stable maps to p^1 x p^1 have picard number exactly 3 for genus g >= 2. Our proof introduces a novel filtration technique combined with deformation-theoretic arguments that resolve a long-standing open question in the field.

We establish new results concerning mirror symmetry in the context of grassmannian, resolving a question that has remained open since it was first posed in the literature. Our approach combines techniques from bps invariants with careful analysis of degeneration phenomena to construct explicit examples and derive sharp bounds.