Degenerate complex structures on surfaces and stability conditions

@misc{robotis2026degenerate,
  title = {{Degenerate complex structures on surfaces and stability conditions}},
  author = {Antonios-Alexandros Robotis and Nicolás Vilches},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.40035},
  eprint = {2610.40035},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.40035},
}

TY  - UNPB
TI  - Degenerate complex structures on surfaces and stability conditions
AU  - Antonios-Alexandros Robotis
AU  - Nicolás Vilches
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2610.40035
UR  - https://arxiv.org/abs/2610.40035
AB  - Physical heuristics suggest that the space of Bridgeland stability conditions of a projective Calabi-Yau manifold X should be related to the moduli space of complex structures on its mirror X^∨. On the other hand, recent work in the literature introduces a modular partial compactification, 𝒜Stab(X), of a quotient of the space of stability conditions on 𝒟^b(X). We provide some mathematical evidence for the aforementioned heuristics by proving that for curves and surfaces, certain boundary strata in 𝒜Stab(X) describe degenerate complex structures on X^∨. Along the way, we introduce a criterion for producing boundary points of 𝒜Stab(𝒟) when 𝒟 is an arbitrary k-linear triangulated category. As a byproduct, we deduce the existence of Bridgeland stability conditions on certain quotients of the derived categories of K3 and Enriques surfaces.
ER  -