The local/logarithmic correspondence and the degeneration formula for quasimaps

Abstract

We study the relationship between the enumerative geometry of rational curves in local geometries and various versions of maximal contact logarithmic curve counts. Our approach is via quasimap theory, and we show versions of the arXiv:1712.05210 local/logarithmic correspondence for quasimaps, and in particular for normal crossings settings, where the Gromov-Witten theoretic formulation of the correspondence fails. The results suggest a link between different formulations of relative Gromov-Witten theory for simple normal crossings divisors via the mirror map. The main results follow from a rank reduction strategy, together with a new degeneration formula for quasimaps.

arXiv comment37 pages, 4 figures, comments welcome

References in corpus (14)

• The intrinsic normal cone
• The moduli space of stable quotients
• Moduli stacks of stable toric quasimaps
• Tropical refined curve counting from higher genera and lambda classes
• Local Gromov-Witten Invariants are Log Invariants
• The canonical wall structure and intrinsic mirror symmetry
• Intersection Theory on Tropicalizations of Toroidal Embeddings
• Stable maps to Looijenga pairs
• Log mirror symmetry and local mirror symmetry
• Holomorphic anomaly equation for $({\mathbb{P}}^2,E)$ and the Nekrasov-Shatashvili limit of local ${\mathbb{P}}^2$
• Higher genus relative and orbifold Gromov-Witten invariants
• On the log-local principle for the toric boundary
• Relative quasimaps and mirror formulae
• The local-orbifold correspondence for simple normal crossings pairs

Cited by in corpus (1)

• The log-open correspondence for two-component Looijenga pairs