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On the quantum periods of del Pezzo surfaces with 1/3 (1,1) singularities
Stockholm University, Faculty of Science, Department of Mathematics.
Number of Authors: 22018 (English)In: Advances in Geometry, ISSN 1615-715X, E-ISSN 1615-7168, Vol. 18, no 3, p. 303-336Article in journal (Refereed) Published
Abstract [en]

In earlier joint work with collaborators we gave a conjectural classification of a broad class of orbifold del Pezzo surfaces, using Mirror Symmetry. We proposed that del Pezzo surfaces X with isolated cyclic quotient singularities such that X admits a Q-Gorenstein toric degeneration correspond via Mirror Symmetry to maximally mutable Laurent polynomials f in two variables, and that the quantum period of such a surface X, which is a generating function for Gromov-Witten invariants of X, coincides with the classical period of its mirror partner f. In this paper we give strong evidence for this conjecture. Contingent on conjectural generalisations of the Quantum Lefschetz theorem and the Abelian/non-Abelian correspondence, we compute many quantum periods for del Pezzo surfaces with 1/3 (1, 1) singularities. Our computations also give strong evidence for the extension of these two principles to the orbifold setting.

Place, publisher, year, edition, pages
2018. Vol. 18, no 3, p. 303-336
Keywords [en]
Gromov-Witten invariants, quantum cohomology, quantum period, del Pezzo surface
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-159135DOI: 10.1515/advgeom-2017-0048ISI: 000439055300004OAI: oai:DiVA.org:su-159135DiVA, id: diva2:1242937
Available from: 2018-08-29 Created: 2018-08-29 Last updated: 2018-08-29Bibliographically approved

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