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arXiv · 2005.07736

Homology supported in Lagrangian submanifolds in mirror quintic threefolds

Daniel López Garcia
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Abstract

In this note we study homological cycles in the mirror quintic Calabi-Yau threefold which can be realized by special Lagrangian submanifolds. We have used Picard-Lefschetz theory to establish the monodromy action and to study the orbit of Lagrangian vanishing cycles. For many prime numbers $p$ we can compute the orbit modulo $p$. We conjecture that the orbit in homology with coefficients in $\mathbb{Z}$ can be determined by these orbits with coefficients in $\mathbb{Z}_p$.

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Daniel López Garcia. 2020-05-15. Homology supported in Lagrangian submanifolds in mirror quintic threefolds. https://doi.org/10.4153/s0008439520000776

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