Homology supported in Lagrangian submanifolds in mirror quintic threefolds
Canadian mathematical bulletin, Tome 64 (2021) no. 3, pp. 709-724
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In this note, we study homology classes in the mirror quintic Calabi–Yau threefold that 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 $\mathbb {Z}_p$.
Mots-clés :
Lagrangian spheres, mirror quintic threefold, monodromy action, Lefschetz fibration, vanishing cycles
Garcia, Daniel López. Homology supported in Lagrangian submanifolds in mirror quintic threefolds. Canadian mathematical bulletin, Tome 64 (2021) no. 3, pp. 709-724. doi: 10.4153/S0008439520000776
@article{10_4153_S0008439520000776,
author = {Garcia, Daniel L\'opez},
title = {Homology supported in {Lagrangian} submanifolds in mirror quintic threefolds},
journal = {Canadian mathematical bulletin},
pages = {709--724},
year = {2021},
volume = {64},
number = {3},
doi = {10.4153/S0008439520000776},
url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439520000776/}
}
TY - JOUR AU - Garcia, Daniel López TI - Homology supported in Lagrangian submanifolds in mirror quintic threefolds JO - Canadian mathematical bulletin PY - 2021 SP - 709 EP - 724 VL - 64 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.4153/S0008439520000776/ DO - 10.4153/S0008439520000776 ID - 10_4153_S0008439520000776 ER -
%0 Journal Article %A Garcia, Daniel López %T Homology supported in Lagrangian submanifolds in mirror quintic threefolds %J Canadian mathematical bulletin %D 2021 %P 709-724 %V 64 %N 3 %U http://geodesic.mathdoc.fr/articles/10.4153/S0008439520000776/ %R 10.4153/S0008439520000776 %F 10_4153_S0008439520000776
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