Intersection theory on Deligne-Mumford compactifications

Eduard Looijenga

Séminaire Bourbaki (1992-1993)

  • Volume: 35, page 187-212
  • ISSN: 0303-1179

How to cite


Looijenga, Eduard. "Intersection theory on Deligne-Mumford compactifications." Séminaire Bourbaki 35 (1992-1993): 187-212. <>.

author = {Looijenga, Eduard},
journal = {Séminaire Bourbaki},
keywords = {intersection theory; Deligne-Mumford compactifications; moduli space; K- dV hierarchy},
language = {eng},
pages = {187-212},
publisher = {Société Mathématique de France},
title = {Intersection theory on Deligne-Mumford compactifications},
url = {},
volume = {35},
year = {1992-1993},

AU - Looijenga, Eduard
TI - Intersection theory on Deligne-Mumford compactifications
JO - Séminaire Bourbaki
PY - 1992-1993
PB - Société Mathématique de France
VL - 35
SP - 187
EP - 212
LA - eng
KW - intersection theory; Deligne-Mumford compactifications; moduli space; K- dV hierarchy
UR -
ER -


  1. 1. D. Bessis, C. Itzykson, J.-B. Zuber: Quantum field theory techniques in graphical enumeration, Adv. Appl. Math.1 (1980), 109-157. Zbl0453.05035MR603127
  2. 2. P. Deligne, D. Mumford: The irreducibility of the space of curves of given genus, 36 (1969), 431-451. Zbl0181.48803MR262240
  3. 3. R. Dijkgraaf: Intersection theory, integrable hierarchies and topological field theories, preprint IAS Princeton (1991). 
  4. 4. R. Dijkgraaf, E. Verlinde, H. Verlinde: Loop equations and Virasoro constraints in nonperturbative two-dimensional quantum gravity, Nucl. Phys. B 348 (1991), 435-456. MR1083914
  5. 5. P. Di Francesco, C. Itzykson, J.-B. Zuber: Polynomial Averages in the Kontsevich model, Comm. Math. Phys.151 (1993), 193-219. Zbl0831.14010MR1201660
  6. 6. M. Fukama, H. Kawai, R. Nakayama: Continuum Schwinger-Dyson equations and universal structures in two-dimensional quantum gravity: conformal gauge, Int. J. Mod. Phys. A6 (1991), 1385-1406. MR1093776
  7. 7. A. Grothendieck: Esquisse d'un programme, preprint (1984). 
  8. 8. Harish- Chandra: Differential operators on a semisimple Lie algebra, Am. J. Math.79 (1957), 87-120. Zbl0072.01901MR84104
  9. 9. J.L. Harer: The virtual cohomological dimension of the mapping class group, Invent. Math. 84 (1986), 157-176. Zbl0592.57009MR830043
  10. 10. J. Hubbard, H. Masur: Quadratic differentials and foliations, Acta Math.142 (1979), 221-274. Zbl0415.30038MR523212
  11. 11. C. Itzykson, J.-B. Zuber: Combinatorics of the modular group II, the Kontsevich integrals, Int. J. Mod. Phys. A 7 (1992), 5661-5705. Zbl0972.14500MR1180858
  12. 12. V.G. Kac: Infinite dimensional Lie algebras (3rd edition), Cambridge U.P., Cambridge, (1990). Zbl0716.17022MR1104219
  13. 13. V.G. Kac, A. Schwartz: Geometric interpretation of the partition function of 2D gravity, Phys. Lett.257 (1991), 329-334. MR1100639
  14. 14. F.F. Knudsen: The projectivity of the moduli space of stable curves II, III, Math. Scand.52 (1983), 161-212. Zbl0544.14020MR702953
  15. 15. M. Kontsevich: Intersection theory on the moduli space of curves, Funct. Anal. and Appl.25 (1991), 123-128. Zbl0742.14021MR1142208
  16. 16. M. Kontsevich: Intersection theory on the moduli space of curves and the matrix Airy function, Comm. Math. Phys.147 (1992), 1-23. Zbl0756.35081MR1171758
  17. 17. D. Mumford: Towards an enumerative geometry of the moduli space of curves, in Arithmetic and Geometry II, M. Artin, J. Tate eds. Birkhäuser PM36 (1983), 271-328. Zbl0554.14008MR717614
  18. 18. R.C. Penner: Perturbative series and the moduli space of punctured surfaces, J. Diff. Geom.27 (1988), 35-53. Zbl0608.30046MR918455
  19. 19. G.B. Shabat, V.A. Voedodsky: Drawing curves over number fields, in The Grothendieck Festschrift III, P. Cartier et al. eds. Birkhäuser PM88 (1990), 199-227. Zbl0790.14026MR1106916
  20. 20. K. Strebel: Quadratic differentials, Springer, Berlin, (1984). Zbl0547.30001MR743423
  21. 21. G.B. Segal, G. Wilson: Loop groups and equations of KdV type, Publ. Math. IHES61 (1985), 5-65. Zbl0592.35112MR783348
  22. 22. E. Witten: Two dimensional gravity and intersection theory on moduli space, Surveys in Diff. Geom.1 (1991), 243-310. MR1144529
  23. 23. E. Witten: On the Kontsevich model and other model and other models of two dimensional gravity, preprint IAS Princeton (1991). 
  24. 24. E. Witten: The N matrix model and gauged WZW models, Nucl. Phys. B371 (1992), 191-245. MR1156705
  25. 25. E. Witten: Algebraic geometry associated with matrix models of two dimensional gravity, preprint IAS Princeton (1991). MR1215968

NotesEmbed ?


You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.


Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.