Álvarez López, Jesús AntonioGilkey, Peter B.2024-02-052024-02-052021-06-21Álvarez López, J.A., Gilkey, P.B. (2021). The Witten deformation of the Dolbeault complex. "J. Geom.", vol. 112, 25, 20 pp.http://hdl.handle.net/10347/32299We introduce a Witten-Novikov type perturbation $\bar\partial_{\bar\omega}$ of the Dolbeault complex of any complex K\"ahler manifold, defined by a form $\omega$ of type $(1,0)$ with $\partial\omega=0$. We give an explicit description of the associated index density which shows that it exhibits a nontrivial dependence on $\omega$. The heat invariants of lower order are shown to be zero.engAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Witten deformationlocal index densityDolbeault complexKähler manifold110206 Fundamentos de matemáticasjournal article10.1007/s00022-021-00589-0open access