Scalar field localization on 3-branes placed at a warped resolved conifold

We have studied the localization of scalar field on a 3-brane embedded in a six dimensional warped bulk of the form $M_4\times C_2$, where $M_4$ is a 3-brane and $C_2$ is a 2-cycle of a six resolved conifold ${\mathcal{C}}_6$ over a $T^{1,1}$ space. Since the resolved conifold is singularity-free in $r=0$ depending on a resolution parameter $a$, we have analyzed the behavior of the localization of scalar field when we vary the resolution parameter. On one hand, this enable us to study the effects that a singularity has on the field. On the other hand we can use the resolution parameter as a fine-tuning between the bulk Planck mass and 3-brane Planck mass and so it opens a new perspective to extend the hierarchy problem. Using a linear and a nonlinear warp factor, we have found that the massive and massless modes are trapped to the brane even in the singular cone ($a\mathrm{\ne }0$). We have also compared the results obtained in this geometry and those obtained in other six-dimensional models, as string-like geometry and cigar-like universe geometry.