[Invariants énumératifs de genre un avec une structure complexe fixée pour des surfaces de del Pezzo]
Nous obtenons une formule pour le nombre de courbes de genre un avec une structure complexe fixée, de degré donné, et passant par un nombre approprié de points génériques de la surface. La solution est exprimée comme la différence entre l'invariant symplectique et un nombre d'intersection sur l'espace de modules de courbes rationnelles.
We obtain a formula for the number of genus one curves with a fixed complex structure of a given degree on a del-Pezzo surface that pass through an appropriate number of generic points of the surface. This enumerative problem is expressed as the difference between the symplectic invariant and an intersection number on the moduli space of rational curves.
Accepté le :
Publié le :
@article{CRMATH_2016__354_5_517_0,
author = {Biswas, Indranil and Mukherjee, Ritwik and Thakre, Varun},
title = {Genus one enumerative invariants in {del-Pezzo} surfaces with a fixed complex structure},
journal = {Comptes Rendus. Math\'ematique},
pages = {517--521},
publisher = {Elsevier},
volume = {354},
number = {5},
year = {2016},
doi = {10.1016/j.crma.2016.02.009},
language = {en},
url = {http://archive.numdam.org/articles/10.1016/j.crma.2016.02.009/}
}
TY - JOUR AU - Biswas, Indranil AU - Mukherjee, Ritwik AU - Thakre, Varun TI - Genus one enumerative invariants in del-Pezzo surfaces with a fixed complex structure JO - Comptes Rendus. Mathématique PY - 2016 SP - 517 EP - 521 VL - 354 IS - 5 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2016.02.009/ DO - 10.1016/j.crma.2016.02.009 LA - en ID - CRMATH_2016__354_5_517_0 ER -
%0 Journal Article %A Biswas, Indranil %A Mukherjee, Ritwik %A Thakre, Varun %T Genus one enumerative invariants in del-Pezzo surfaces with a fixed complex structure %J Comptes Rendus. Mathématique %D 2016 %P 517-521 %V 354 %N 5 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2016.02.009/ %R 10.1016/j.crma.2016.02.009 %G en %F CRMATH_2016__354_5_517_0
Biswas, Indranil; Mukherjee, Ritwik; Thakre, Varun. Genus one enumerative invariants in del-Pezzo surfaces with a fixed complex structure. Comptes Rendus. Mathématique, Tome 354 (2016) no. 5, pp. 517-521. doi : 10.1016/j.crma.2016.02.009. http://archive.numdam.org/articles/10.1016/j.crma.2016.02.009/
[1] How many smooth plane cubics with given j-invariant are tangent to 8 lines in general position?, Contemp. Math., Volume 123 (1991), pp. 15-29
[2] The quantum cohomology of blow-ups of and enumerative geometry, J. Differ. Geom., Volume 48 (1998), pp. 61-90
[3] Mirror Symmetry, Clay Math. Inst. AMS, 2003
[4] Genus-one enumerative invariants in with fixed j-invariant, Duke Math. J., Volume 94 (1998), pp. 279-324
[5] Counting tropical elliptic plane curves with fixed j-invariant, Comment. Math. Helv., Volume 84 (2009), pp. 387-427
[6] Gromov–Witten classes, quantum cohomology, and enumerative geometry, Mirror Symmetry, II, AMS/IP Stud. Adv. Math., vol. 1, Amer. Math. Soc., Providence, RI, 1997, pp. 607-653
[7] Enumerative geometry of elliptic curves on toric surfaces | arXiv
[8] Counting elliptic plane curves with fixed j-invariant, Proc. Amer. Math. Soc., Volume 125 (1997), pp. 3471-3479
[9] A mathematical theory of quantum cohomology, J. Differ. Geom., Volume 42 (1995), pp. 259-367
[10] Enumeration of genus-two curves with a fixed complex structure in and , J. Differ. Geom., Volume 65 (2003), pp. 341-467
[11] Enumeration of one-nodal rational curves in projective spaces, Topology, Volume 4 (2004), pp. 793-829
[12] Enumerative versus symplectic invariants, J. Symplectic Geom., Volume 2 (2004), pp. 445-543
[13] A. Zinger, Personal communication.
Cité par Sources :
