Enumerative Geometry of Calabi-Yau 5-Folds

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dc.creatorPandharipande, R.
dc.creatorZinger, A.
dc.date2008-02-12
dc.date.accessioned2026-07-07T09:20:15Z
dc.date.available2026-07-07T09:20:15Z
dc.descriptionGromov-Witten theory is used to define an enumerative geometry of curves in Calabi-Yau 5-folds. We find recursions for meeting numbers of genus 0 curves, and we determine the contributions of moving multiple covers of genus 0 curves to the genus 1 Gromov-Witten invariants. The resulting invariants, conjectured to be integral, are analogous to the previously defined BPS counts for Calabi-Yau 3 and 4-folds. We comment on the situation in higher dimensions where new issues arise. Two main examples are considered: the local Calabi-Yau P^2 with balanced normal bundle 3O(-1) and the compact Calabi-Yau hypersurface X_7 in P^6. In the former case, a closed form for our integer invariants has been conjectured by G. Martin. In the latter case, we recover in low degrees the classical enumeration of elliptic curves by Ellingsrud and Stromme.
dc.description40 pages, 3 tables, 6 figures
dc.identifierhttps://arxiv.org/abs/0802.1640
dc.identifierhttp://arxiv.org/abs/0802.1640
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/154662
dc.subjectAlgebraic Geometry
dc.subjectSymplectic Geometry
dc.subject14N35, 53D45
dc.titleEnumerative Geometry of Calabi-Yau 5-Folds
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