What question did this study set out to answer?

The research aims to establish the relationship between Hamiltonian isotopy and stability conditions within specific Lagrangian sections of Calabi-Yau manifolds.

December 21, 2025Open Access

Nakai-Moishezon criteria and the toric Thomas-Yau conjecture

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JSJacopo StoppaScuola Internazionale Superiore di Studi Avanzati

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Implication

This paper demonstrates the role of stability conditions in establishing Hamiltonian isotopies for Lagrangian sections in Fano manifolds' mirror spaces.

Key Points

The research aims to establish the relationship between Hamiltonian isotopy and stability conditions within specific Lagrangian sections of Calabi-Yau manifolds.
Analyzed Hamiltonian isotopies of Lagrangian sections in Calabi-Yau Lagrangian fibrations.
Used the SYZ transform and toric homological mirror symmetry to explore deformed Hermitian Yang-Mills connections.
Evaluated Bridgeland stable objects within the Fukaya-Seidel category.
Applied findings to toric weak del Pezzo surfaces and projective plane configurations.
Proved that Hamiltonian isotopy occurs if and only if a stability condition is satisfied.
Showed that Bridgeland stable conditions lead to Hamiltonian isotopies to special Lagrangian sections.
Provided conditions under which Bridgeland instability results in weak solutions of special Lagrangian equations.

Cite This Study

Jacopo Stoppa (2025) studied this question.

synapsesocial.com/papers/69473b64db9c958d0dfca7ba https://doi.org/10.48550/arxiv.2505.07228

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Implication

This paper demonstrates the role of stability conditions in establishing Hamiltonian isotopies for Lagrangian sections in Fano manifolds' mirror spaces.

Nakai-Moishezon criteria and the toric Thomas-Yau conjecture

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Implication

Key Points

Cite This Study

Nakai-Moishezon criteria and the toric Thomas-Yau conjecture

Discussion

Member takes

Implication

Key Points

Cite This Study

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