Geodesic
Quantum Riemann–Roch, Lefschetz and Serre
Thomas Coates1 ; Alexander Givental2
1 Department of Mathematics, Harvard University, Cambridge, MA 02138, United States
2 Department of Mathematics, University of California Berkeley, Berkeley CA 94720, United States
Annals of mathematics, Tome 165 (2007) no. 1, pp. 15-53.

Voir la notice de l'article provenant de la source Annals of Mathematics website

Given a holomorphic vector bundle $E$ over a compact Kähler manifold $X$, one defines twisted Gromov-Witten invariants of $X$ to be intersection numbers in moduli spaces of stable maps $f:\Sigma \to X$ with the cap product of the virtual fundamental class and a chosen multiplicative invertible characteristic class of the virtual vector bundle $H^0(\Sigma,f^* E) \ominus H^1(\Sigma,f^* E)$. Using the formalism of quantized quadratic Hamiltonians [25], we express the descendant potential for the twisted theory in terms of that for $X$. This result (Theorem $1$) is a consequence of Mumford’s Grothendieck-Riemann-Roch theorem applied to the universal family over the moduli space of stable maps. It determines all twisted Gromov-Witten invariants, of all genera, in terms of untwisted invariants.
DOI : 10.4007/annals.2007.165.15

Thomas Coates 1 ; Alexander Givental 2

1 Department of Mathematics, Harvard University, Cambridge, MA 02138, United States
2 Department of Mathematics, University of California Berkeley, Berkeley CA 94720, United States 
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Thomas Coates; Alexander Givental. Quantum Riemann–Roch, Lefschetz and Serre. Annals of mathematics, Tome 165 (2007) no. 1, pp. 15-53. doi : 10.4007/annals.2007.165.15. http://geodesic.mathdoc.fr/articles/10.4007/annals.2007.165.15/

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