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October 20, 2025Open Access

Stability conditions on Calabi-Yau threefolds via Brill-Noether theory of curves

Key Points

Proving the Brill-Noether-type inequality ensures Bridgeland stability conditions can exist on Calabi-Yau threefolds.
The approach applies to a wide range of Calabi-Yau threefolds, including those formed as complete intersections.
A polarised Calabi-Yau threefold is essential for verifying the necessary inequalities for stability conditions.
The findings contribute to expanding the understanding of stability in algebraic geometry, particularly in relation to Calabi-Yau varieties.

Abstract

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.

Stability conditions on Calabi-Yau threefolds via Brill-Noether theory of curves

Key Points

Abstract

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