A detailed investigation of the excited states accessed by UV absorption in alternating DNA duplexes was performed by means of an extensive sampling of intra- and intermolecular degrees of freedom. The excited states were computed using the algebraic diagrammatic construction method to second-order (ADC(2)). A realistic DNA environment was included through an electrostatic embedding QM/MM coupling scheme. The results indicate that (i) most excited states are delocalized over at most two bases, (ii) charge transfer states are located at higher energies than the bright states in the Franck-Condon region, but (iii) coupling between locally excited and charge transfer states may provide a route to dynamical charge separation, and (iv) spectral broadening is mainly caused by intramolecular vibrations.