This approach verifies a Brill-Noether-type inequality in Calabi-Yau threefolds, suggesting existence of Bridgeland stability conditions.
Fix a polarised Calabi-Yau threefold $(X,H)$. We reduce a version of the Bayer-Macrì-Toda conjecture for $(X,H)$, which ensures the existence of Bridgeland stability conditions on X, to verifying a Brill-Noether-type inequality for curves on X. We then prove this inequality for a broad class of Calabi-Yau threefolds, including complete intersection Calabi-Yau threefolds in weighted projective spaces.
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Feyzbakhsh et al. (2025) studied this question.
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