We define and study a family of cubic surfaces in the projectivized tangent bundle over a four dimensional projective space associated to the root system D5. The 27 lines are rational over the base and we determine the classifying map to the moduli space of marked cubic surfaces. This map has degree two and we use it to get short proofs for some results on the Chow group of the moduli space of marked cubic surfaces.
A family of marked cubic surfaces and the root system D_5 / E. Colombo, B. van Geemen. - In: INTERNATIONAL JOURNAL OF MATHEMATICS. - ISSN 0129-167X. - 18:5(2007 May), pp. 505-525. [10.1142/S0129167X07004163]
A family of marked cubic surfaces and the root system D_5
E. Colombo;B. van Geemen
2007
Abstract
We define and study a family of cubic surfaces in the projectivized tangent bundle over a four dimensional projective space associated to the root system D5. The 27 lines are rational over the base and we determine the classifying map to the moduli space of marked cubic surfaces. This map has degree two and we use it to get short proofs for some results on the Chow group of the moduli space of marked cubic surfaces.
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