Stable maps to Looijenga pairs: orbifold examples

Pierrick Bousseau; Andrea Brini; Michel van Garrel

doi:10.1007/s11005-021-01451-9

Stable maps to Looijenga pairs: orbifold examples

Pierrick Bousseau, Andrea Brini, Michel van Garrel

Mathematics

Research output: Contribution to journal › Article › peer-review

26 Downloads (Pure)

Abstract

In [15], we established a series of correspondences relating five enumerative theories of log Calabi–Yau surfaces, i.e. pairs (Y, D) with Y a smooth projective complex surface and D= D ₁+ ⋯ + D _l an anticanonical divisor on Y with each D _i smooth and nef. In this paper, we explore the generalisation to Y being a smooth Deligne–Mumford stack with projective coarse moduli space of dimension 2 and D _i nef Q-Cartier divisors. We consider in particular three infinite families of orbifold log Calabi–Yau surfaces, and for each of them, we provide closed-form solutions of the maximal contact log Gromov–Witten theory of the pair (Y, D), the local Gromov–Witten theory of the total space of ⨁ _iO _Y(- D _i) , and the open Gromov–Witten of toric orbi-branes in a Calabi–Yau 3-orbifold associated with (Y, D). We also consider new examples of BPS integral structures underlying these invariants and relate them to the Donaldson–Thomas theory of a symmetric quiver specified by (Y, D) and to a class of open/closed BPS invariants.

Original language	English
Article number	109
Number of pages	37
Journal	Letters in Mathematical Physics
Volume	111
Issue number	4
DOIs	https://doi.org/10.1007/s11005-021-01451-9
Publication status	Published - 9 Aug 2021

Bibliographical note

Funding Information:
This project has been supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No. 746554 (M. vG.), the Engineering and Physical Sciences Research Council under Grant Agreement ref. EP/S003657/2 (A. B.) and by Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation (P. B. and M. vG.)

Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Nature B.V.

Keywords

Gromov-Witten invariants
Log Calabi-Yau surfaces
Orbifolds
Donaldson-Thomas invariants

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

Access to Document

10.1007/s11005-021-01451-9

BousseauP2021Stable
Bousseau, P., Brini, A. & Garrel, M.v. Stable maps to Looijenga pairs: orbifold examples. Lett Math Phys 111, 109 (2021). https://doi.org/10.1007/s11005-021-01451-9 This document is subject the Springer Nature reuse terms: https://www.springer.com/gp/open-access/publication-policies/aam-terms-of-use
Accepted author manuscript, 564 KBLicence: Other (please specify with Rights Statement)

Cite this

@article{21d81efea9db4085861077367f618abe,

title = "Stable maps to Looijenga pairs: orbifold examples",

abstract = "In [15], we established a series of correspondences relating five enumerative theories of log Calabi–Yau surfaces, i.e. pairs (Y, D) with Y a smooth projective complex surface and D= D 1+ ⋯ + D l an anticanonical divisor on Y with each D i smooth and nef. In this paper, we explore the generalisation to Y being a smooth Deligne–Mumford stack with projective coarse moduli space of dimension 2 and D i nef Q-Cartier divisors. We consider in particular three infinite families of orbifold log Calabi–Yau surfaces, and for each of them, we provide closed-form solutions of the maximal contact log Gromov–Witten theory of the pair (Y, D), the local Gromov–Witten theory of the total space of ⨁ iO Y(- D i) , and the open Gromov–Witten of toric orbi-branes in a Calabi–Yau 3-orbifold associated with (Y, D). We also consider new examples of BPS integral structures underlying these invariants and relate them to the Donaldson–Thomas theory of a symmetric quiver specified by (Y, D) and to a class of open/closed BPS invariants. ",

keywords = "Gromov-Witten invariants, Log Calabi-Yau surfaces, Orbifolds, Donaldson-Thomas invariants",

author = "Pierrick Bousseau and Andrea Brini and {van Garrel}, Michel",

note = "Funding Information: This project has been supported by the European Union{\textquoteright}s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No. 746554 (M. vG.), the Engineering and Physical Sciences Research Council under Grant Agreement ref. EP/S003657/2 (A. B.) and by Dr. Max R{\"o}ssler, the Walter Haefner Foundation and the ETH Z{\"u}rich Foundation (P. B. and M. vG.) Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer Nature B.V.",

year = "2021",

month = aug,

day = "9",

doi = "10.1007/s11005-021-01451-9",

language = "English",

volume = "111",

journal = "Letters in Mathematical Physics",

issn = "1573-0530",

publisher = "Springer",

number = "4",

}

TY - JOUR

T1 - Stable maps to Looijenga pairs

T2 - orbifold examples

AU - Bousseau, Pierrick

AU - Brini, Andrea

AU - van Garrel, Michel

N1 - Funding Information: This project has been supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No. 746554 (M. vG.), the Engineering and Physical Sciences Research Council under Grant Agreement ref. EP/S003657/2 (A. B.) and by Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation (P. B. and M. vG.) Publisher Copyright: © 2021, The Author(s), under exclusive licence to Springer Nature B.V.

PY - 2021/8/9

Y1 - 2021/8/9

N2 - In [15], we established a series of correspondences relating five enumerative theories of log Calabi–Yau surfaces, i.e. pairs (Y, D) with Y a smooth projective complex surface and D= D 1+ ⋯ + D l an anticanonical divisor on Y with each D i smooth and nef. In this paper, we explore the generalisation to Y being a smooth Deligne–Mumford stack with projective coarse moduli space of dimension 2 and D i nef Q-Cartier divisors. We consider in particular three infinite families of orbifold log Calabi–Yau surfaces, and for each of them, we provide closed-form solutions of the maximal contact log Gromov–Witten theory of the pair (Y, D), the local Gromov–Witten theory of the total space of ⨁ iO Y(- D i) , and the open Gromov–Witten of toric orbi-branes in a Calabi–Yau 3-orbifold associated with (Y, D). We also consider new examples of BPS integral structures underlying these invariants and relate them to the Donaldson–Thomas theory of a symmetric quiver specified by (Y, D) and to a class of open/closed BPS invariants.

AB - In [15], we established a series of correspondences relating five enumerative theories of log Calabi–Yau surfaces, i.e. pairs (Y, D) with Y a smooth projective complex surface and D= D 1+ ⋯ + D l an anticanonical divisor on Y with each D i smooth and nef. In this paper, we explore the generalisation to Y being a smooth Deligne–Mumford stack with projective coarse moduli space of dimension 2 and D i nef Q-Cartier divisors. We consider in particular three infinite families of orbifold log Calabi–Yau surfaces, and for each of them, we provide closed-form solutions of the maximal contact log Gromov–Witten theory of the pair (Y, D), the local Gromov–Witten theory of the total space of ⨁ iO Y(- D i) , and the open Gromov–Witten of toric orbi-branes in a Calabi–Yau 3-orbifold associated with (Y, D). We also consider new examples of BPS integral structures underlying these invariants and relate them to the Donaldson–Thomas theory of a symmetric quiver specified by (Y, D) and to a class of open/closed BPS invariants.

KW - Gromov-Witten invariants

KW - Log Calabi-Yau surfaces

KW - Orbifolds

KW - Donaldson-Thomas invariants

UR - http://www.scopus.com/inward/record.url?scp=85112069312&partnerID=8YFLogxK

U2 - 10.1007/s11005-021-01451-9

DO - 10.1007/s11005-021-01451-9

M3 - Article

SN - 1573-0530

VL - 111

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

IS - 4

M1 - 109

ER -

Stable maps to Looijenga pairs: orbifold examples

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Fingerprint

Cite this