Autoren:	Mak, Cheuk Yu Ruddat, Helge
Titel:	Tropically constructed Lagrangians in mirror quintic threefolds
Online-Publikationsdatum:	7-Dez-2020
Erscheinungsdatum:	2020
Sprache des Dokuments:	Englisch
Zusammenfassung/Abstract:	We use tropical curves and toric degeneration techniques to construct closed embedded Lagrangian rational homology spheres in a lot of Calabi-Yau threefolds. The homology spheres are mirror dual to the holomorphic curves contributing to the Gromov-Witten (GW) invariants. In view of Joyce’s conjecture, these Lagrangians are expected to have special Lagrangian representatives and hence solve a special Lagrangian enumerative problem in Calabi-Yau threefolds. We apply this construction to the tropical curves obtained from the 2,875 lines on the quintic Calabi-Yau threefold. Each admissible tropical curve gives a Lagrangian rational homology sphere in the corresponding mirror quintic threefold and the Joyce’s weight of each of these Lagrangians equals the multiplicity of the corresponding tropical curve. As applications, we show that disjoint curves give pairwise homologous but non-Hamiltonian isotopic Lagrangians and we check in an example that >300 mutually disjoint curves (and hence Lagrangians) arise. Dehn twists along these Lagrangians generate an abelian subgroup of the symplectic mapping class group with that rank.
DDC-Sachgruppe:	510 Mathematik 510 Mathematics
Veröffentlichende Institution:	Johannes Gutenberg-Universität Mainz
Organisationseinheit:	FB 08 Physik, Mathematik u. Informatik
Veröffentlichungsort:	Mainz
ROR:	https://ror.org/023b0x485
DOI:	http://doi.org/10.25358/openscience-5464
Version:	Published version
Publikationstyp:	Zeitschriftenaufsatz
Nutzungsrechte:	CC BY
Informationen zu den Nutzungsrechten:	https://creativecommons.org/licenses/by/4.0/
Zeitschrift:	Forum of mathematics : Sigma 8
Seitenzahl oder Artikelnummer:	e58
Verlag:	Cambridge Univ. Press
Verlagsort:	Cambridge
ISSN:	2050-5094
URL der Originalveröffentlichung:	https://doi.org/10.1017/fms.2020.54
DOI der Originalveröffentlichung:	10.1017/fms.2020.54
Enthalten in den Sammlungen:	JGU-Publikationen