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We study the effects of the integrated galactic initial mass function (IGIMF)and dust evolution on the abundance patterns of high redshift starburstgalaxies. In our chemical models, the rapid collapse of gas clouds triggers anintense and rapid star formation episode, which lasts until the onset of agalactic wind, powered by the thermal energy injected by stellar winds andsupernova explosions. Our models follow the evolution of several chemicalelements (C, N, $\alpha$-elements and Fe) both in the gas and dust phases. %Themost recent stellar yield and dust prescriptions are adopted. We test differentvalues of $\beta$, the slope of the embedded cluster mass function for theIGIMF, where lower $\beta$ values imply a more top-heavy initial mass function(IMF). The computed abundances are compared to high-quality abundancemeasurements obtained in lensed galaxies and from composite spectra in largesamples of star-forming galaxies in the redshift range $2 \lesssim z \lesssim3$. The adoption of the IGIMF causes a sensible increase of the rate of starformation with respect to a standard Salpeter IMF, with a strong impact onchemical evolution. We find that in order to reproduce the observed abundancepatterns in these galaxies, either we need a very top-heavy IGIMF ($\beta < 2$)or large amounts of dust. In particular, if dust is important, the IGIMF shouldhave $\beta \ge 2$, which means an IMF slightly more top-heavy than theSalpeter one. The evolution of the dust mass with time for galaxies ofdifferent mass and IMF is also computed, highlighting that the dust amountincreases with a top-heavier IGIMF.

The influence of a top-heavy integrated galactic IMF and dust on the chemical evolution of high-redshift starbursts