Hodge integrals and degenerate contributions

Abstract

Degenerate contributions to higher genus Gromov-Witten invariants of Calabi-Yau 3-folds are computed via Hodge integrals. The vanishing of contributions of covers of elliptic curves conjectured by Gopakumar and Vafa is proven. A formula for degree 1 covers for all genus pairs is computed in agreement with M-theoretic calculations of Gopakumar and Vafa. Finally, these results lead to a proof of a formula in the tautological ring of the moduli space of curves previously conjectured by Faber.

21 pages, LaTeX2e. Expanded discussion of relationships with the M-theoretic calculations of Gopakumar-Vafa. New results for arbitrary 3-folds following a suggestion of Jinzenji and Xiong

References in corpus (5)

• Counting higher genus curves in a Calabi-Yau manifold
• Local Mirror Symmetry at Higher Genus
• M-Theory and Topological Strings--I
• M-Theory and Topological Strings--II
• Enumerative geometry of hyperelliptic plane curves

Cited by in corpus (54)

• Curve counting via stable pairs in the derived category
• Gromov-Witten theory, Hurwitz numbers, and Matrix models, I
• The moduli space of stable quotients
• Enumerative geometry of Calabi-Yau 4-folds
• Three questions in Gromov-Witten theory
• The tropical vertex
• BPS states of curves in Calabi--Yau 3--folds
• Local Mirror Symmetry at Higher Genus
• Relative Lefschetz Action and BPS State Counting
• 13/2 ways of counting curves
• Tropical refined curve counting from higher genera and lambda classes
• Kuranishi homology and Kuranishi cohomology
• Gromov-Witten/Donaldson-Thomas correspondence for toric 3-folds
• The moduli space of curves, double Hurwitz numbers, and Faber's intersection number conjecture
• Gromov-Witten, Gopakumar-Vafa, and Donaldson-Thomas invariants of Calabi-Yau threefolds
• Curves in Calabi-Yau 3-folds and Topological Quantum Field Theory
• BCOV's Feynman rule of quintic $3$-folds
• Logarithmic series and Hodge integrals in the tautological ring (with an appendix by D. Zagier)
• Counting embedded curves in symplectic 6-manifolds
• Computing top intersections in the tautological ring of $M_g$
• Reduced Genus-One Gromov-Witten Invariants
• Gopakumar-Vafa invariants via vanishing cycles
• Geometric Aspects of Mirror Symmetry (with SYZ for Rigid CY manifolds)
• The local Gromov-Witten invariants of configurations of rational curves
• A Comparison Theorem for Gromov-Witten Invariants in the Symplectic Category
• Multiple covers and the integrality conjecture for rational curves in Calabi-Yau threefolds
• Virasoro constraints for target curves
• Three dimensional tropical correspondence formula
• Enumerative Geometry of Calabi-Yau 5-Folds
• The Gopakumar-Vafa finiteness conjecture
• A splitting of the virtual class for genus one stable maps
• Embedding property of $J$-holomorphic curves in Calabi-Yau manifolds for generic $J$
• The local Gromov-Witten theory of curves
• Notes on the proof of the KKV conjecture
• Modular compactifications of ${\mathcal{M}}_{2,n}$ with Gorenstein singularities
• On the rigidity of stable maps to Calabi-Yau threefolds
• Log BPS numbers of log Calabi-Yau surfaces
• Topological Strings, Two-Dimensional Yang-Mills Theory and Chern-Simons Theory on Torus Bundles
• A compactification of the space of maps from curves
• Holomorphic Anomaly Equation and BPS State Counting of Rational Elliptic Surface
• Counting planar curves in ${\mathbb{P}}^3$ with degenerate singularities
• Hodge integrals, partition matrices, and the lambda_g conjecture
• The closed topological vertex via the Cremona transform
• Lower Bounds for Enumerative Counts of Positive-Genus Real Curves
• Super-rigidity and finiteness of embedded $J$-holomorphic curves on Calabi-Yau threefolds
• Elliptic Virtual Structure Constants and Generalizations of BCOV-Zinger Formula to Projective Fano Hypersurfaces
• The Aspinwall-Morrison calculation and Gromov-Witten theory
• Super-rigid Donaldson-Thomas invariants
• Degree One Contributions and Open Gromov-Witten Invariants
• Gopakumar-Vafa BPS invariants, Hilbert schemes and quasimodular forms. I
• Evidence for a conjecture of Pandharipande
• Mirror symmetry for concavex vector bundles on projective spaces
• Gromov-Witten Theory and Threshold Corrections
• On finiteness and rigidity of J-holomorphic curves in symplectic three-folds