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Article Dans Une Revue Transactions of the American Mathematical Society Année : 2019

Triple planes with $p_g=q=0$

Résumé

We show that general triple planes with genus and irregularity zero belong to at most 12 families, that we call surfaces of type I to XII, and we prove that the corresponding Tschirnhausen bundle is a direct sum of two line bundles in cases I, II, III, whereas it is a rank 2 Steiner bundle in the remaining cases. We also provide existence results and explicit descriptions for surfaces of type I to VII, recovering all classical examples and discovering several new ones. In particular, triple planes of type VII provide counterexamples to a wrong claim made in 1942 by Bronowski. Finally, in the last part of the paper we discuss some moduli problems related to our constructions.

Dates et versions

hal-01961582 , version 1 (20-12-2018)

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Daniele Faenzi, Francesco Polizzi, Jean Vallès. Triple planes with $p_g=q=0$. Transactions of the American Mathematical Society, 2019, 371, pp.589-639. ⟨10.1090/tran/7276⟩. ⟨hal-01961582⟩
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