A proof of the gottsche-yau-zaslow formula

Yu-Jong Tzeng Harvard University

mathscidoc:1609.10260

Journal of Differential Geometry, 90, (3), 439-472, 2012
Let S be a complex smooth projective surface and L be a line bundle on S. G¨ottsche conjectured that for every integer r, the number of r-nodal curves in |L| is a universal polynomial of four topological numbers when L is sufficiently ample. We prove G¨ottsche’s conjecture using the algebraic cobordism group of line bundles on surfaces and degeneration of Hilbert schemes of points. In addition, we prove the G¨ottsche-Yau-Zaslow Formula which expresses the generating function of the numbers of nodal curves in terms of quasimodular forms and two unknown series.
No keywords uploaded!
[ Download ] [ 2016-09-13 22:47:21 uploaded by admin ] [ 657 downloads ] [ 0 comments ] [ Cited by 13 ]
@inproceedings{yu-jong2012a,
  title={A PROOF OF THE GOTTSCHE-YAU-ZASLOW FORMULA},
  author={Yu-Jong Tzeng},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160913224721602576922},
  booktitle={Journal of Differential Geometry},
  volume={90},
  number={3},
  pages={439-472},
  year={2012},
}
Yu-Jong Tzeng. A PROOF OF THE GOTTSCHE-YAU-ZASLOW FORMULA. 2012. Vol. 90. In Journal of Differential Geometry. pp.439-472. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160913224721602576922.
Please log in for comment!
 
 
Contact us: office-iccm@tsinghua.edu.cn | Copyright Reserved