{
"id": "1712.02331",
"version": "v1",
"published": "2017-12-06T18:54:52.000Z",
"updated": "2017-12-06T18:54:52.000Z",
"title": "Connecting Hodge integrals to Gromov-Witten invariants by Virasoro operators",
"authors": [
"Xiaobo Liu",
"Haijiang Yu"
],
"comment": "21 pages",
"categories": [
"math.AG",
"math-ph",
"math.DG",
"math.MP"
],
"abstract": "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.",
"revisions": [
{
"version": "v1",
"updated": "2017-12-06T18:54:52.000Z"
}
],
"analyses": {
"keywords": [
"connecting hodge integrals",
"gromov-witten invariants",
"virasoro operators",
"point case",
"generating function"
],
"note": {
"typesetting": "TeX",
"pages": 21,
"language": "en",
"license": "arXiv",
"status": "editable"
}
}
}