A descendent relation in genus 2

Pavel Belorousski; Rahul Pandharipande

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2000)

  • Volume: 29, Issue: 1, page 171-191
  • ISSN: 0391-173X

How to cite


Belorousski, Pavel, and Pandharipande, Rahul. "A descendent relation in genus 2." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 29.1 (2000): 171-191. <http://eudml.org/doc/84400>.

author = {Belorousski, Pavel, Pandharipande, Rahul},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {codimension 2 relation; descendent strata; moduli space of stable 3-pointed genus 2 curves; genus 2 gravitational potentials; Gromov-Witten theory; WDVV-equations; Getzler's equations; projective plane},
language = {eng},
number = {1},
pages = {171-191},
publisher = {Scuola normale superiore},
title = {A descendent relation in genus 2},
url = {http://eudml.org/doc/84400},
volume = {29},
year = {2000},

AU - Belorousski, Pavel
AU - Pandharipande, Rahul
TI - A descendent relation in genus 2
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2000
PB - Scuola normale superiore
VL - 29
IS - 1
SP - 171
EP - 191
LA - eng
KW - codimension 2 relation; descendent strata; moduli space of stable 3-pointed genus 2 curves; genus 2 gravitational potentials; Gromov-Witten theory; WDVV-equations; Getzler's equations; projective plane
UR - http://eudml.org/doc/84400
ER -


  1. [AV] D. Abramovich - A. Vistoli, in preparation. 
  2. [BM] K. Behrend - YU. MANIN, Stacks of stable maps and Gromov-Witten invariants, Duke Math. J.85 (1996), 1-60. Zbl0872.14019MR1412436
  3. [B] P. Belorousski, Chow rings of moduli spaces of pointed elliptic curves, Ph.D. thesis, University of Chicago, 1998. 
  4. [CH] L. Caporaso - J. Harris, Counting plane curves of any genus, Invent. Math.131 (1998), 345-392. Zbl0934.14040MR1608583
  5. [D] B. Dubrovin, Geometry of 2D topological field theories, In "Integrable Systems and Quantum Groups" (Montecatini Terme, 1993), Lecture Notes in Math. 1620, Springer, Berlin, 1996, pp. 120-348. Zbl0841.58065MR1397274
  6. [DZ] B. Dubrovin - Y. Zhang, Bihamiltonian hierarchies in 2D Topological Field Theory at one-loop approximation, preprint, hep-th/9712232. 
  7. [EHX] T. Eguchi - K. Hori - C.-S. Xiong, Quantum cohomology and Virasoro algebra, Phys. Lett. B402 (1997), 71-80. Zbl0933.81050MR1454328
  8. [EX] T. Eguchi - C.-S. Xiong, Quantum cohomology at higher genus: toplogical recursion relations and virasoro conditions, Adv. Theor. Math. Phys.2 (1998), 219-229. Zbl0910.32033MR1635867
  9. [EH] D. Eisenbud - J. Harris, The Kodaira dimension of the moduli space of curves of genus ≽ 23, Invent. Math.90 (1987), 359-387. Zbl0631.14023
  10. [Fa] C. Faber, Algorithms for computing intersection numbers on moduli spaces of curves, with an application to the class of the locus of Jacobians, preprint, alg-geom/9706006. MR1714822
  11. [FP] W. Fulton - R. Pandharipande, Notes on stable maps and quantum cohomology, Algebraic Geometry-Santa Cruz1995, 45-96, Proc. Sympos. Pure Math., 62, Part 2, Amer. Math. Soc., Providence, RI, 1997. Zbl0898.14018MR1492534
  12. [G1] E. Getzler, Intersection theory on M1,4 and elliptic Gromov-Witten invariants, J. Amer. Math. Soc.10 (1997), 973-998. Zbl0909.14002MR1451505
  13. [G2] E. Getzler, Topological recursion relations in genus 2, in "Integrable systems and algebraic geometry (Kobe/Kyoto, 1997)", World Sci. Publishing, River Edge, NJ, pp. 73-106. Zbl1021.81056MR1672112
  14. [Gi] A. Givental, Equivariant Gromov-Witten invariants, Internat. Math. Res. Notices1996, no. 13, 613-663. Zbl0881.55006MR1408320
  15. [Gr] T. Graber, Ph.D. thesis, UCLA, 1998. 
  16. [GP1] T. Graber - R. Pandharipande, Localization of virtual classes, Invent. Math.135 (1999), 487-518. Zbl0953.14035MR1666787
  17. [GP2] T. Graber - R. Pandharipande, in preparation. 
  18. [HM] J. Harris - D. Mumford, On the Kodaira dimension of the moduli space of curves, Invent. Math.67 (1982), 23-86. Zbl0506.14016MR664324
  19. [KK] A. Kabanov - T. Kimura, Intersection numbers and rank one Cohomological Field Theories in genus one, Comm. Math. Phys.194 (1998), 651-674. Zbl0974.14018MR1631493
  20. [Ke] S. Keel, Intersection theory of moduli space of stable N-pointed curves of genus zero, Trans. Amer. Math. Soc.330 (1992), 545-574. Zbl0768.14002MR1034665
  21. [Ko] M. Kontsevich, Enumeration of rational curves via torus actions, In "The moduli Space of Curves", R. Dijkgraaf - C. Faber - G. van der Geer (eds.) Birkhauser, 1995, pp. 335-368. Zbl0885.14028MR1363062
  22. [KM1] M. Kontsevich - YU. Manin, Gromov-Witten classes, quantum cohomology, and enumerative geometry, Commun. Math. Phys.164 (1994), 525-562. Zbl0853.14020MR1291244
  23. [KM2] M. Kontsevich - YU. Manin, Quantum cohomology of a product, with an appendix by R. Kaufmann, Invent. Math.124 (1996), 313-339. Zbl0853.14021MR1369420
  24. [KM3] M. Kontsevich - YU. Manin, Relations between the correlators of the topological sigma-model coupled to gravity, Comm. Math. Phys.196 (1998), 385-398. Zbl0946.14032MR1645019
  25. [P] R. Pandharipande, A Geometric Construction of Getzler's Relation in H*(M1,4, Q), Math. Ann.313 (1999), 715-729 (electronic). Zbl0933.14035MR1686935
  26. [R] Z. Ran, The degree of a Severi variety, Bull. Amer. Math. Soc.17 (1987), 125-128. Zbl0629.14020MR888887
  27. [RT1] Y. Ruan - G. Tian, A mathematical theory of quantum cohomology, J. Diff. Geom.42 (1995), 259-367. Zbl0860.58005MR1366548
  28. [RT2] Y. Ruan - G. Tian, Higher genus symplectic invariants and sigma model coupled with gravity, Invent. Math.130 (1997), 455-516. Zbl0904.58066MR1483992
  29. [V] A. Vistoli, Chow groups of quotient varieties, J. Algebra107 (1987), 410-424. Zbl0627.14005MR885804
  30. [W] E. Witten, Two-dimensional gravity and intersection theory on moduli space, Surveys in differential geometry (Cambridge, MA, 1990), 243-310. Zbl0757.53049MR1144529

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