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.
The Chow group of the moduli space of marked cubic surfaces / E. Colombo, B. Van Geemen. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - 183:3(2004), pp. 291-316. [10.1007/s10231-003-0097-x]
The Chow group of the moduli space of marked cubic surfaces
E. ColomboPrimo
;B. Van GeemenUltimo
2004
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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