Embeddings and disjunction of Lagrangian pinwheels via rational blow-ups
Abstract
We use the symplectic rational blow-up to study some Lagrangian pinwheels in symplectic rational manifolds. In particular, we determine which symplectic forms in the threefold blow-up of $\mathbb{C} P^2$ carry Lagrangian projective planes that can be made disjoint by a Hamiltonian isotopy. In addition, we show that such a disjunction is not possible in del Pezzo surfaces with Euler characteristic between $4$ and $7$. Finally, we determine which symplectic forms on $S^2\times S^2$ carry a Lagrangian $L_{3,1}$ pinwheel, answering a question of J. Evans.
Fields of Study & Subjects
Dynamics and Control of Mechanical Systems
Mechanics and Biomechanics Studies
Robotic Mechanisms and Dynamics
Publication details
- Journal / source
- Journal of Symplectic Geometry
- Volume
- 24
- Issue
- 1
- Pages
- 105–129
- Publication date
- 1 January 2026
- Language
- EN