• Corpus ID: 116949875

A Degeneration formula of Gromov-Witten invariants with respect to a curve class for degenerations from blow-ups

@article{Liu2004ADF,
  title={A Degeneration formula of Gromov-Witten invariants with respect to a curve class for degenerations from blow-ups},
  author={Chien‐Hao Liu and Shing-Tung Yau},
  journal={arXiv: Algebraic Geometry},
  year={2004}
}

• Chien‐Hao Liu, S. Yau
• Published 11 August 2004
• Mathematics
• arXiv: Algebraic Geometry

In two very detailed, technical, and fundamental works, Jun Li constructed a theory of Gromov-Witten invariants for a singular scheme of the gluing form Y1 ∪D Y2 that arises from a degeneration W/A 1 and a theory of relative Gromov-Witten invariants for a codimension-1 relative pair (Y,D). As a summit, he derived a degeneration formula that relates a finite summation of the usual Gromov-Witten invariants of a general smooth fiber Wt of W/A 1 to the Gromov-Witten invariants of the singular fiber W0 = Y1 ∪D Y2 via gluing the relative pairs (Y1,D) and (Y2,D). The finite sum mentioned above depends on a relative ample line bundle H on W/A 1 . His theory has already applications to string theory and mathematics alike. For other new applications of Jun Li’s theory, one needs a refined degeneration formula that depends