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Stability conditions on Calabi-Yau threefolds of type K

  • Uttaran Dutta
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Abstract

A Calabi-Yau threefold of type K is a free quotient X=(S× E)/G of the product of a K3 surface and an elliptic curve. We construct a family of geometric Bridgeland stability conditions on X by using Liu's product construction on S× E and then inducing along the Galois covering. The family has dimension 2h1,1(X), and is disjoint from the GL̃2+(R)-orbit of Li's stability conditions. These threefolds carry a K3 fibration, and the pushforward of an object from a smooth K3 fiber is (semi)stable if and only if it is (semi)stable on the K3 surface.

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Cite

BibTeXRIS
BibTeX
@misc{dutta2026stability,
  title = {{Stability conditions on Calabi-Yau threefolds of type K}},
  author = {Uttaran Dutta},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.38298},
  eprint = {2610.38298},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.38298},
}
RIS
TY  - UNPB
TI  - Stability conditions on Calabi-Yau threefolds of type K
AU  - Uttaran Dutta
PY  - 2026
DA  - 2026/10/28
PB  - arXiv
DO  - 10.48550/arxiv.2610.38298
UR  - https://arxiv.org/abs/2610.38298
AB  - A Calabi-Yau threefold of type K is a free quotient X=(S× E)/G of the product of a K3 surface and an elliptic curve. We construct a family of geometric Bridgeland stability conditions on X by using Liu's product construction on S× E and then inducing along the Galois covering. The family has dimension 2h^1,1(X), and is disjoint from the GL̃_2^+(R)-orbit of Li's stability conditions. These threefolds carry a K3 fibration, and the pushforward of an object from a smooth K3 fiber is (semi)stable if and only if it is (semi)stable on the K3 surface.
ER  -