Geodesic
Compactifying the space of stable maps
Abramovich, Dan1 ; Vistoli, Angelo2
1Department of Mathematics, Boston University, 111 Cummington Street, Boston, Massachusetts 02215
2Dipartimento di Matematica, Università di Bologna, Piazza di Porta San Donato 5, 40127 Bologna, Italy
Journal of the American Mathematical Society, Tome 15 (2002) no. 1, pp. 27-75
Cet article a éte moissonné depuis la source American Mathematical Society

Voir la notice de l'article

In this paper we study a notion of twisted stable map, from a curve to a tame Deligne-Mumford stack, which generalizes the well-known notion of stable map to a projective variety.
DOI : 10.1090/S0894-0347-01-00380-0

Abramovich, Dan  1   ; Vistoli, Angelo  2

1 Department of Mathematics, Boston University, 111 Cummington Street, Boston, Massachusetts 02215
2 Dipartimento di Matematica, Università di Bologna, Piazza di Porta San Donato 5, 40127 Bologna, Italy 
@article{10_1090_S0894_0347_01_00380_0,
     author = {Abramovich, Dan and Vistoli, Angelo},
     title = {Compactifying the space of stable maps},
     journal = {Journal of the American Mathematical Society},
     pages = {27--75},
     year = {2002},
     volume = {15},
     number = {1},
     doi = {10.1090/S0894-0347-01-00380-0},
     url = {http://geodesic.mathdoc.fr/articles/10.1090/S0894-0347-01-00380-0/}
}
TY  - JOUR
AU  - Abramovich, Dan
AU  - Vistoli, Angelo
TI  - Compactifying the space of stable maps
JO  - Journal of the American Mathematical Society
PY  - 2002
SP  - 27
EP  - 75
VL  - 15
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.1090/S0894-0347-01-00380-0/
DO  - 10.1090/S0894-0347-01-00380-0
ID  - 10_1090_S0894_0347_01_00380_0
ER  - 
%0 Journal Article
%A Abramovich, Dan
%A Vistoli, Angelo
%T Compactifying the space of stable maps
%J Journal of the American Mathematical Society
%D 2002
%P 27-75
%V 15
%N 1
%U http://geodesic.mathdoc.fr/articles/10.1090/S0894-0347-01-00380-0/
%R 10.1090/S0894-0347-01-00380-0
%F 10_1090_S0894_0347_01_00380_0
Abramovich, Dan; Vistoli, Angelo. Compactifying the space of stable maps. Journal of the American Mathematical Society, Tome 15 (2002) no. 1, pp. 27-75. doi: 10.1090/S0894-0347-01-00380-0

[1] Abramovich, Dan, Oort, Frans Alterations and resolution of singularities 2000 39 108

[2] Artin, M. Versal deformations and algebraic stacks Invent. Math. 1974 165 189

[3] Behrend, K., Manin, Yu. Stacks of stable maps and Gromov-Witten invariants Duke Math. J. 1996 1 60

[4] Théorie des intersections et théorème de Riemann-Roch 1971

[5] Deligne, P., Mumford, D. The irreducibility of the space of curves of given genus Inst. Hautes Études Sci. Publ. Math. 1969 75 109

[6] Edidin, Dan, Graham, William Equivariant intersection theory Invent. Math. 1998 595 634

[7] Fulton, W., Pandharipande, R. Notes on stable maps and quantum cohomology 1997 45 96

[8] Hirsch, K. A. On skew-groups Proc. London Math. Soc. 1939 357 368

[9] Grothendieck, Alexander Fondements de la géométrie algébrique. [Extraits du Séminaire Bourbaki, 1957–1962.] 1962

[10] Revêtements étales et groupe fondamental 1971

[11] Epstein, Leo F. A function related to the series for 𝑒^{𝑒^{𝑥}} J. Math. Phys. Mass. Inst. Tech. 1939 153 173

[12] De Jong, A. J., Oort, F. On extending families of curves J. Algebraic Geom. 1997 545 562

[13] Keel, Seán, Mori, Shigefumi Quotients by groupoids Ann. of Math. (2) 1997 193 213

[14] Kelly, G. M., Street, Ross Review of the elements of 2-categories 1974 75 103

[15] Knutson, Donald Algebraic spaces 1971

[16] Kontsevich, Maxim Enumeration of rational curves via torus actions 1995 335 368

[17] Kresch, Andrew Cycle groups for Artin stacks Invent. Math. 1999 495 536

[18] Laumon, Gérard, Moret-Bailly, Laurent Champs algébriques 2000

[19] Matsumura, Hideyuki Commutative ring theory 1989

[20] Milne, James S. Étale cohomology 1980

[21] Mochizuki, Shinichi Extending families of curves over log regular schemes J. Reine Angew. Math. 1999 43 71

[22] Vistoli, Angelo Intersection theory on algebraic stacks and on their moduli spaces Invent. Math. 1989 613 670

Cité par Sources :