Moduli Spaces of Higher Spin Curves and Integrable Hierarchies

Compositio Mathematica

Volumn 126, Issue 2, 2001, Pages 157-212

  Jarvis, Tyler J ^a   Kimura, Takashi ^b   Vaintrob, Arkady ^c  

^a BRIGHAM YOUNG UNIVERSITY   (United States)

^b USA   (United States)

^c UNIVERSITY OF OREGON   (United States)

Author keywords

Cohomological field theories; Frobenius manifolds; Generalized witten conjecture; Higher spin curves; Integrable hierarchies

Indexed keywords

EID: 0013507517     PISSN: 0010437X     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1017528003622     Document Type: Article

References (36)

1. p-gravity, Comm. Math. Phys. 147 (1992), 25-56.
2. Arbarello, E. and Cornalba, M.: The Picard groups of the moduli spaces of curves, Topology 26(2) (1987), 153-171.
3. Belorousski, P. and Pandharipande, R.: A descendent relation in genus 2, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 29 (2000), 171-191, math.AG/9803072.
4. Deligne, P.: Le déterminant de la cohomologie, In: Current Trends in Arithmetical Algebraic Geometry (Arcata, Calif., 1985), Contemp. Math. 67, Amer. Math. Soc., Providence, RI, 1987, pp. 93-177.
5. Dijkgraaf, R. and Witten, E.: Mean field theory, topological field theory, and multi-matrix models, Nucl. Phys. B 342 (1990), 486-522.
6. Dubrovin, B.: Geometry of 2D topological field theories, In: Integrable Systems and Quantum Groups, Lecture Notes in Math. 1620, Springer, Berlin, 1996.
7. Dubrovin, B. and Zhang, Y.: Bihamiltonian hierarchies in 2D topological field theory at one-loop approximation, Commun. Math. Phys. 198 (1998), 311-361.
8. Eguchi, T., Hori, K. and Xiong, C. S.: Quantum cohomology and the Virasoro algebra, hep-th/9703086.
9. Faber, C. and Pandharipande, R.: Hodge integrals and Gromov-Witten theory, Phys. Lett. B402 (1997), 71-80, math.AG/9810173.
10. g conjecture, Invent. Math. 139 (2000), 173-199, math.AG/9908052.
11. Fulton, W. and Pandharipande, R.: Notes on stable maps and quantum cohomology, Proc. Sympos. Pure. Math. 62, Part 2, Amer. Math. Soc., 1987, 45-96, alg-geom/9608011.
12. 1,4 and elliptic Gromov-Witten invariants, J. Amer. Math. Soc. 10(4) (1997), 973-998. alg-geom/9612009.
13. Getzler, E.: Topological recursion relations in genus 2. In: Integrable Systems and Algebraic Geometry, World. Sci. Publ., 1998, pp. 73-106, math.AG/9801003.
14. Getzler, E. and Kapranov, M.: Modular operads, Compositio Math. 110(1) (1998), 65-126. dg-ga/9408003.
15. Getzler, E. and Pandharipande, R.: Virasoro constraints and the Chern classes of the Hodge bundle, Nuclear Phys. B530 (1998), 701-714, math.AG/9805114.
16. Hitchin, N.: Frobenius manifolds, In: J. Hurtubise and F. Lalonde (eds), Gauge Theory and Symplectic Geometry, NATO-ASO Series C: 488 (1997), Kluwer, Boston.
17. Jarvis, T. J.: Geometry of the moduli of higher spin curves, Internat. J. Math. 11(5) (2000), 637-663, math.AG/9809138.
18. Jarvis, T. J.: Torsion-free sheaves and moduli of generalized spin curves, Compositio Math. 110(3) (1998), 291-333.
19. Jarvis, T. J.: Picard group of the moduli of higher spin curves, Brigham Young University preprint, math.AG/9908085.
20. Jarvis, T. J., Kimura, T. and Vaintrob, A.: Stable spin maps, Gromov-Witten invariants, and quantum cohomology, math.AG/0012210.
21. Kabanov, A. and Kimura, T.: Intersection numbers and rank one cohomological field theories in genus one, Comm. Math. Phys. 194 (1998), 651-674. alg-geom/9706003.
22. Keel, S.: Intersection theory of moduli spaces of stable n-pointed curves of genus zero, Trans. Amer. Math. Soc. 330 (1992), 545-574.
23. Kontsevich, M.: Intersection theory on the moduli space of curves and the matrix Airy function, Comm. Math. Phys. 147 (1992), 1-23.
24. Kontsevich, M. and Manin, Yu. I.: Gromov-Witten classes, quantum cohomology, and enumerative geometry, Comm. Math. Phys. 164 (1994), 525-562.
25. Krichever, I. M.: The τ-function of the universal Whitham hierarchy, matrix models and topological field theories, Comm. Pure Appl. Math. 47(4) (1994), 437-475.
26. Looijenga, E.: Intersection theory on Deligne-Mumford compactifications [after Witten and Kontsevich], Séminaire Bourbaki, Vol. 1992/93, Astérisque 216 (1993), 187-212.
27. Manin, Yu. I.: In: Frobenius Manifolds, Quantum Cohomology, and Moduli Spaces, Amer. Math. Soc., Providence, RI, 1999.
28. Manin, Yu. I.: Three constructions of Frobenius manifolds: a comparative study, Asian J. Math. 3 (1999), 179-220, math.AG/9801006.
29. Manin, Yu. I. and Zograf, P.: Invertible cohomological field theories and Weil-Petersson volumes, Ann. Inst. Fourier 50, (2000), 519-535, math.AG/9902051.
30. Mumford, D.: Theta characteristics of an algebraic curve, Ann. Sci. École Norm. Sup. 4 (1971), 181-192.
31. Mumford, D.: Towards an enumerative geometry of the moduli space of curves, In: M. Artin and J. Tate (eds), Arithmetic and Geometry, Part II, Progr. Math. 36, Birkhäuser, Basel, 1983, pp. 271-328.
32. Ruan, Y. and Tian, G.: A mathematical theory of quantum cohomology, J. Differential Geom. 42 (1995), 259-367.
33. Srinivas, V.: In: Algebraic K-Theory, Progr. Math. 90, Birkhäuser, Boston, 1996.
34. Witten, E.: Algebraic geometry associated with matrix models of two-dimensional gravity, Topological Methods in Modern Mathematics (Stony Brook, NY, 1991), Publish or Perish, Houston, TX, 1993, pp. 235-269.
35. Witten, E.: The N-matrix model and gauged WZW models, Nuclear Phys. B 371(1-2) (1992), 191-245.
36. Witten, E.: Two-dimensional gravity and intersection theory on moduli space, Surveys Differential Geom. 1 (1991), 243-310.