Reduced classes and curve counting on surfaces I: theory

2011/12/31 by M. Kool, Martijn Kool, Richard Thomas +1 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic Geometry and Number Theory #Bundle #Canonical bundle #Combinatorics #Computer science #Conjecture #Geometric and Algebraic Topology #Geometry #Homotopy and Cohomology in Algebraic Topology #Locus (genetics) #Mathematics #Moduli space #Property (philosophy) #Pure mathematics #Section (typography) #Space (punctuation) #Surface (topology) #Zero (linguistics) #hep-th #math.AG #msc:14N35

paper · pdf · doi:10.14231/ag-2014-017

published as Algebraic Geometry 1, 334-383, 2014 · 54 pages. Typo fixed

openalex publication_date 2014/06/30 · arxiv created 2016/05/09 · arxiv updated 2016/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We develop a theory of reduced Gromov-Witten and stable pair invariants of surfaces and their canonical bundles.

Citations

• Gromov-Witten invariants of varieties with holomorphic 2-forms
• Gromov-Witten theory and Noether-Lefschetz theory
• Derived algebraic geometry, determinants of perfect complexes, and applications to obstruction theories for maps and complexes
• A Semiregularity Map for Modules and Applications to Deformations
• A theory of generalized Donaldson-Thomas invariants
• Family Gromov-Witten Invariants for Kahler Surfaces

Cited by

• Degeneracy loci, virtual cycles and nested Hilbert schemes II