Abstract
Naruki gave an explicit construction of the moduli space of marked cubic surfaces, starting from a toric variety and proceeding with blow-ups and contractions. Using his result, we compute the Chow groups and the Chern classes of this moduli space. As an application we relate a recent result of Freitag on the Hilbert polynomial of a certain ring of modular forms to the Riemann–Roch theorem for the moduli space.
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