Comptes Rendus
no. 5
Algebraic geometry
Genus one enumerative invariants in del-Pezzo surfaces with a fixed complex structure

Presented by: Claire Voisin

Indranil Biswas1; Ritwik Mukherjee1; Varun Thakre2
1 School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
2 Department of Mathematics, Harish Chandra Research Institute, Allahabad 211019, India
Comptes Rendus. Mathématique, Volume 354 (2016) no. 5, pp. 517-521.

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.

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2016.02.009

Indranil Biswas 1; Ritwik Mukherjee 1; Varun Thakre 2

1 School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
2 Department of Mathematics, Harish Chandra Research Institute, Allahabad 211019, India 
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Indranil Biswas; Ritwik Mukherjee; Varun Thakre. Genus one enumerative invariants in del-Pezzo surfaces with a fixed complex structure. Comptes Rendus. Mathématique, Volume 354 (2016) no. 5, pp. 517-521. doi : 10.1016/j.crma.2016.02.009. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.02.009/

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