A Note on a Generalization of the Multiple Cover Formula and the Simple Flop

REFERENCES

• Bershadsky , M. , Cecotti , S. , Ooguri , H. , Vafa , C. ( 1993 ). Holomorphic anomalies in topological field theories (with an appendix by S. Katz) . Nucl. Phys. B 405 : 279 – 304 .
   Web of Science ®Google Scholar
• Bryan , J. , Graber , T. ( 2009 ). The Crepant Resolution Conjecture. In: Algebraic Geometry: Seattle 2005 (Proceedings of Symposia in Pure Mathematics). Vol. 80–1. Providence, RI: American Mathematical Society, pp. 23–42 .
   Google Scholar
• Faber , C. , Pandharipande , R. ( 2000 ). Hodge integrals and Gromov-Witten theory . Invent. Math. 139 ( 1 ): 173 – 199 .
   Web of Science ®Google Scholar
• Graber , T. , Pandharipande , R. ( 1999 ). Localization of virtual classes . Invent. Math. 135 ( 2 ): 487 – 518 .
   Web of Science ®Google Scholar
• Hori , K. , Katz , S. , Klemm , A. , Pandharipande , R. , Thomas , R. , Vafa , C. , Vakil , R. , Zaslow , E. ( 2003 ). Mirror Symmetry . Clay Mathematics Monographs. Providence , RI : American Mathematical Society .
   Google Scholar
• Iwao , Y. , Lee , Y.-P. , Lin , H.-W. , Wang , C.-L. ( 2012 ). Invariance of Gromov-Witten theory under a simple flop . J. Reine Angew. Math. 663 : 67 – 90 .
   Web of Science ®Google Scholar
• Kollár , J. , Mori , S. ( 1998 ). Birational geometry of algebraic varieties. With the collaboration of C. H. Clemens and A. Corti. In: Cambridge Tracts in Mathematics. Vol. 134. Cambridge: Cambridge University Press .
   Google Scholar
• Lee , Y.-P. , Lin , H.-W. , Wang , C.-L. ( 2010 ). Flops, motives and invariance of quantum rings . Ann. of Math. 172 ( 1 ): 243 – 290 .
   Web of Science ®Google Scholar
• Ruan , Y. ( 2006 ). The cohomology ring of crepant resolutions of orbifolds. In: Gromov-Witten Theory of Spin Curves and Orbifolds. Volume 403 of Contemp. Math., Providence, RI: American Mathematical Society, pp. 117–126 .
   Google Scholar
• Communicated by L. Ein.
   Google Scholar