The resolved chemical abundance properties within the interstellar
  medium of star-forming galaxies at $\mathbf{ \textit{z} \approx 1.5}$
  We exploit the unprecedented depth of integral field data from the KMOS
Ultra-deep Rotational Velocity Survey (KURVS) to analyse the strong (H$\alpha$)
and forbidden ([NII], [SII]) emission line ratios in 22 main-sequence galaxies
at $z\approx1.5$. Using the [NII]/H$\alpha$ emission-line ratio we confirm the
presence of the stellar mass $-$ gas-phase metallicity relation at this epoch,
with galaxies exhibiting on average 0.13$\pm$0.04 dex lower gas-phase
metallicity (12+log(O/H)$_{\rm M13}$=8.40$\pm$0.03) for a given stellar mass
($\log_{10}$($M_{\rm *}$[$M_{\odot}$]=10.1$\pm$0.1) than local main-sequence
galaxies. We determine the galaxy-integrated [SII] doublet ratio, with a median
value of [SII]$\lambda$6716/$\lambda$6731=1.26$\pm$0.14 equivalent to an
electron density of log$_{10}$($n_{\rm e}$[cm$^{-3}$])=1.95$\pm$0.12. Utilising
CANDELS $HST$ multi-band imaging we define the pixel surface-mass and
star-formation rate density in each galaxy and spatially resolve the
fundamental metallicity relation at $z\approx1.5$, finding an evolution of
0.05$\pm$0.01 dex compared to the local relation. We quantify the intrinsic
gas-phase metallicity gradient within the galaxies using the [NII]/H$\alpha$
calibration, finding a median annuli-based gradient of
$\Delta$Z/$\Delta$R=$-$0.015$\pm$0.005 dex kpc$^{-1}$. Finally we examine the
azimuthal variations in gas-phase metallicity, which show a negative
correlation with the galaxy integrated star-formation rate surface density
($r_{\rm s}$=$-$0.40, $p_{\rm s}$=0.07) but no connection to the galaxies
kinematic or morphological properties nor radial variations in stellar mass
surface density or star formation rate surface density. This suggests both the
radial and azimuthal variations in interstellar medium properties are connected
to the galaxy integrated density of recent star formation.
