Year: 2026
Type: preprint
Abstract: We consider objects in the Fukaya category of a class of K3 surfaces defined by certain Lagrangian spheres. Assuming that homological mirror symmetry for K3 surfaces holds with sufficiently strong (expected) properties, we prove that, in this case, stability with respect to a suitable Bridgeland stability condition implies the existence of an isomorphic special Lagrangian sphere, as predicted by the general Thomas-Yau-Joyce conjectures. In particular this holds unconditionally for suitable quartic surfaces in $\mathbb{P}^3$ or sextics in $\mathbb{P}(3,1,1,1)$ and their mirrors. A variant holds on the Calabi-Yau threefolds obtained by taking the product of our K3 surfaces with an elliptic curve. These seem to be the first results of this type on compact manifolds.
Source: arXiv (Cornell University)
Author: Stoppa, Jacopo
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7215075796