no. 17-18
Géométrie algébrique
Parties polaires et compactification ELSV

Présenté par : Claire Voisin

Dudin, Bashar1
1 Laboratoire Manceau de mathématiques, avenue Olivier-Messiaen, 72085 Le Mans cedex 9, France
Comptes Rendus. Mathématique, Tome 351 (2013) no. 17-18, pp. 695-698.

On propose une construction alternative à une compactification – due à [6] – du champ des courbes lisses munies de fonctions méromorphes dʼordres fixés. Cette dernière est obtenue comme lʼadhérence du champ de départ dans un champ propre ; on donne une description modulaire des points du bord.

We give an alternative construction to a compactification—due to [6]—of the stack of smooth curves endowed with a meromorphic function having poles with fixed order. The original compactification is described as a closure of the initial stack in a proper stack; we give a modular description of the boundary points.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2013.09.004
Dudin, Bashar 1

1 Laboratoire Manceau de mathématiques, avenue Olivier-Messiaen, 72085 Le Mans cedex 9, France 
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Dudin, Bashar. Parties polaires et compactification ELSV. Comptes Rendus. Mathématique, Tome 351 (2013) no. 17-18, pp. 695-698. doi : 10.1016/j.crma.2013.09.004. http://www.numdam.org/articles/10.1016/j.crma.2013.09.004/

[1] Abramovich, D.; Olsson, M.; Vistoli, A. Tame stacks in positive characteristic, Ann. Inst. Fourier (Grenoble), Volume 58 (2008) no. 4, pp. 1057-1091

[2] Behrend, K.; Fantechi, B. The intrinsic normal cone, Invent. Math., Volume 128 (1997) no. 1, pp. 45-88

[3] Behrend, K.; Manin, Y. Stacks of stable maps and Gromov–Witten invariants, Duke Math. J., Volume 85 (1996) no. 1, pp. 1-60

[4] Bertin, J.; Romagny, M. Champs de Hurwitz, Mémoires de la SMF, vol. 125/126, Société Mathématique de France, 2011

[5] Deligne, P.; Mumford, D. The irreducibility of the space of curves of given genus, Publ. Math. Inst. Hautes Études Sci., Volume 36 (1969), pp. 75-109

[6] Ekedahl, T.; Lando, S.; Shapiro, M.; Vainshtein, A. Hurwitz numbers and intersections on moduli spaces of curves, Invent. Math., Volume 146 (2001) no. 2, pp. 297-327

[7] Fantechi, B.; Pandharipande, R. Stable maps and branch divisors, Compos. Math., Volume 130 (2002) no. 3, pp. 345-364

[8] Harris, J.; Mumford, D. On the Kodaira dimension of the moduli space of curves, Invent. Math., Volume 67 (1982) no. 1, pp. 23-88

[9] Kempf, G.; Knudsen, F.F.; Mumford, D.; Saint-Donat, B. Toroidal Embeddings. I, Lecture Notes in Mathematics, vol. 339, Springer-Verlag, Berlin, 1973

[10] Romagny, M. Group actions on stacks and applications, Michigan Math. J., Volume 53 (2005) no. 1, pp. 209-236

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