Stable maps to Looijenga pairs: orbifold examples

Abstract

In arXiv:2011.08830 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 $D=D_1+\cdots +D_l$ 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 $\mathbb{Q}$-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 ${⨁}_i{\mathcal{O}}_Y(-D_i)$, and the open Gromov-Witten theory of toric orbi-branes in a Calabi-Yau 3-orbifold associated to $(Y,D)$. 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.

arXiv comment26 pages, 11 figures. v2: typos fixed, minor changes, version accepted for the Boris Dubrovin Memorial Issue of LMP

References in corpus (32)

• The Topological Vertex
• Topological Strings and Integrable Hierarchies
• Knot Invariants and Topological Strings
• Mirror Symmetry, D-Branes and Counting Holomorphic Discs
• Knots, links and branes at large N
• Torus knots and mirror symmetry
• Orbifold Quantum Riemann-Roch, Lefschetz and Serre
• Polynomial invariants for torus knots and topological strings
• Computing Genus-Zero Twisted Gromov-Witten Invariants
• Framed knots at large N
• Enumerative geometry of Calabi-Yau 4-folds
• Curves on K3 surfaces and modular forms
• The tropical vertex
• A Mirror Theorem for Toric Stacks
• Cohomological Hall algebra of a symmetric quiver
• Knots-quivers correspondence
• A Mathematical Theory of the Topological Vertex
• Topological Strings, D-Model, and Knot Contact Homology
• Tropical refined curve counting from higher genera and lambda classes
• Genus zero Gopakumar-Vafa type invariants for Calabi-Yau 4-folds
• Local Gromov-Witten Invariants are Log Invariants
• The quantum tropical vertex
• Donaldson-Thomas invariants, torus knots, and lattice paths
• Gromov-Witten/Donaldson-Thomas correspondence for toric 3-folds
• Large N duality, lagrangian cycles, and algebraic knots
• Gromov-Witten theory with maximal contacts
• Open orbifold Gromov-Witten invariants of [C^3/Z_n]: localization and mirror symmetry
• Stable maps to Looijenga pairs
• Stable pair invariants of local Calabi-Yau 4-folds
• Quantum mirrors of log Calabi-Yau surfaces and higher genus curve counting
• On the log-local principle for the toric boundary
• The local-orbifold correspondence for simple normal crossings pairs

Cited by in corpus (2)

• Sheaves of maximal intersection and multiplicities of stable log maps
• Refined open topological strings revisited