The Gaia-ESO survey: A spectroscopic study of the young open cluster NGC 3293

We present a spectroscopic analysis of the GIRAFFE and UVES data collected by the Gaia-ESO survey for the young open cluster NGC 3293. Archive spectra from the same instruments obtained in the framework of the `VLT-FLAMES survey of massive stars' are also analysed. Atmospheric parameters, non-LTE chemical abundances for six elements, or variability information are reported for a total of about 160 B stars spanning a wide range in terms of spectral types (B1 to B9.5) and rotation rate (up to 350 km/s). We take advantage of the multi-epoch observations to detect several binary systems or intrinsically line-profile variables. A deconvolution algorithm is used to infer the current, true (deprojected) rotational velocity distribution. We find a broad, Gaussian-like distribution peaking around 200-250 km/s. Although some stars populate the high-velocity tail, most stars in the cluster appear to rotate far from critical. We discuss the chemical properties of the cluster, including the low occurrence of abundance peculiarities in the late B stars and the paucity of objects showing CN-cycle burning products at their surface. We argue that the former result can largely be explained by the inhibition of diffusion effects because of fast rotation, while the latter is generally in accord with the predictions of single-star evolutionary models under the assumption of a wide range of initial spin rates at the onset of main-sequence evolution. However, we find some evidence for a less efficient mixing in two quite rapidly rotating stars that are among the most massive objects in our sample. Finally, we obtain a cluster age of ~20 Myrs through a detailed, star-to-star correction of our results for the effect of stellar rotation. This is significantly older than previous estimates from turn-off fitting that fully relied on classical, non-rotating isochrones. [abridged]