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Connecting Hodge integrals to Gromov-Witten invariants by Virasoro operators

141   0   0.0 ( 0 )
 Added by Hajiang Yu
 Publication date 2017
  fields Physics
and research's language is English




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In this paper, we show that the generating function for linear Hodge integrals over moduli spaces of stable maps to a nonsingular projective variety $X$ can be connected to the generating function for Gromov-Witten invariants of $X$ by a series of differential operators ${ L_m mid m geq 1 }$ after a suitable change of variables. These operators satisfy the Virasoro bracket relation and can be seen as a generalization of the Virasoro operators appeared in the Virasoro constraints for Kontsevich-Witten tau-function in the point case. This result is an extension of the work in cite{LW} for the point case which solved a conjecture of Alexandrov.



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