Gutenberg Open Science: Tropically constructed Lagrangians in mirror quintic threefolds

Please use this identifier to cite or link to this item: http://doi.org/10.25358/openscience-5464

Full metadata record

DC Field	Value	Language
dc.contributor.author	Mak, Cheuk Yu	-
dc.contributor.author	Ruddat, Helge	-
dc.date.accessioned	2020-12-07T11:22:17Z	-
dc.date.available	2020-12-07T11:22:17Z	-
dc.date.issued	2020	-
dc.identifier.uri	https://openscience.ub.uni-mainz.de/handle/20.500.12030/5468	-
dc.description.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.	en_GB
dc.description.sponsorship	DFG, Open Access-Publizieren Universität Mainz / Universitätsmedizin Mainz	de
dc.language.iso	eng	de
dc.rights	CC BY	*
dc.rights.uri	https://creativecommons.org/licenses/by/4.0/	*
dc.subject.ddc	510 Mathematik	de_DE
dc.subject.ddc	510 Mathematics	en_GB
dc.title	Tropically constructed Lagrangians in mirror quintic threefolds	en_GB
dc.type	Zeitschriftenaufsatz	de
dc.identifier.doi	http://doi.org/10.25358/openscience-5464	-
jgu.type.dinitype	article	en_GB
jgu.type.version	Published version	de
jgu.type.resource	Text	de
jgu.organisation.department	FB 08 Physik, Mathematik u. Informatik	de
jgu.organisation.number	7940	-
jgu.organisation.name	Johannes Gutenberg-Universität Mainz	-
jgu.rights.accessrights	openAccess	-
jgu.journal.title	Forum of mathematics : Sigma	de
jgu.journal.volume	8	de
jgu.pages.alternative	e58	de
jgu.publisher.name	Cambridge Univ. Press	de
jgu.publisher.place	Cambridge	de
jgu.publisher.uri	https://doi.org/10.1017/fms.2020.54	de
jgu.publisher.issn	2050-5094	de
jgu.organisation.place	Mainz	-
jgu.subject.ddccode	510	de
jgu.publisher.doi	10.1017/fms.2020.54
jgu.organisation.ror	https://ror.org/023b0x485
Appears in collections:	JGU-Publikationen

Files in This Item:

	File	Description	Size	Format
	mak_cheuk_yu-tropically_con-20201207104332192.pdf		2.51 MB	Adobe PDF	View/Open

Show simple item record