Degeneration of (-1)-shifted symplectic stacks and categorification of Donaldson-Thomas invariants
Abstract
We study cohomological Donaldson-Thomas invariants of perfect complexes in a semistable degeneration of projective Calabi-Yau threefolds, with smooth components X1,X2 meeting along a smooth anticanonical surface S. The generic fiber of degeneration family is a (−1)-shifted symplectic stack. Over the special fiber, the derived restriction to S is derived Lagrangian, and its homotopy fiber product is also (−1)-shifted symplectic. Our goal is to relate the categorical DT invariants of the generic fiber moduli, induced by periodic cyclic homology of matrix factorization category of 0-shifted potential functions over such moduli, to that of the special fiber obtained via derived Lagrangian intersection and geometric quantization. This is achieved via construction of a flat Gauss-Manin connection that relates the generic fiber cohomological DT invariants to that of the special fiber. The geometric framework, universal trace diagrams, and fourfold foliation were developed jointly with Jacob Kryczka in arXiv:2510.20325. Here we construct ordinary critical realizations, oriented cyclic-to-bar comparisons, and Gauss-Manin operators, and verify finite specialization in explicit moduli problems. We workout our construction via several explicit examples such as Grassmannians, Relative Hilbert Schemes and moduli space of pure 2 dimensional sheaves with support moving in a fixed linear system of divisors in the ambient threefold.
Related
- On logarithmic Donaldson-Thomas invariants for local Calabi-Yau $4$-folds
- The shifted symplectic geometry of derived higher groupoids
- Degenerations of shifted symplectic moduli stacks of sheaves
- Toward Shifted symplectic Chiralization: Deformation of Courant Algebroids
- Shifted Symplectic Fibrations and Derived Thurston Theorem
BibTeX
@misc{sheshmani2026degeneration,
title = {{Degeneration of (-1)-shifted symplectic stacks and categorification of Donaldson-Thomas invariants}},
author = {Artan Sheshmani},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40336},
eprint = {2610.40336},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40336},
}
RIS
TY - UNPB
TI - Degeneration of (-1)-shifted symplectic stacks and categorification of Donaldson-Thomas invariants
AU - Artan Sheshmani
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40336
UR - https://arxiv.org/abs/2610.40336
AB - We study cohomological Donaldson-Thomas invariants of perfect complexes in a semistable degeneration of projective Calabi-Yau threefolds, with smooth components X_1,X_2 meeting along a smooth anticanonical surface S. The generic fiber of degeneration family is a (−1)-shifted symplectic stack. Over the special fiber, the derived restriction to S is derived Lagrangian, and its homotopy fiber product is also (−1)-shifted symplectic. Our goal is to relate the categorical DT invariants of the generic fiber moduli, induced by periodic cyclic homology of matrix factorization category of 0-shifted potential functions over such moduli, to that of the special fiber obtained via derived Lagrangian intersection and geometric quantization. This is achieved via construction of a flat Gauss-Manin connection that relates the generic fiber cohomological DT invariants to that of the special fiber. The geometric framework, universal trace diagrams, and fourfold foliation were developed jointly with Jacob Kryczka in arXiv:2510.20325. Here we construct ordinary critical realizations, oriented cyclic-to-bar comparisons, and Gauss-Manin operators, and verify finite specialization in explicit moduli problems. We workout our construction via several explicit examples such as Grassmannians, Relative Hilbert Schemes and moduli space of pure 2 dimensional sheaves with support moving in a fixed linear system of divisors in the ambient threefold.
ER -