Title: Determination of small<b><i>x</i></b>shadowing corrections at DESY HERA
Abstract: The recent ${F}_{2}$ data can be described using the DGLAP evolution equations with an appropriate choice of input distributions and the choice of the starting scale for the ${Q}^{2}$ evolution. We demonstrate in this paper that we cannot conclude that there are no significant shadowing corrections in the DESY HERA kinematic region using ${F}_{2}$ data only. In this paper we calculate the shadowing corrections to the longitudinal structure function ${F}_{L}{(x,Q}^{2})$ and to the charm component of the proton structure function ${F}_{2}^{c}{(x,Q}^{2})$ in the HERA kinematic region using an eikonal approach. We demonstrate that the shadowing corrections to these observables are very large and that charm production is strongly modified at small $x.$ Our results agree with the few recent H1 data.