Triple planes with $p_g=q=0$

Abstract : 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.
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Contributor : Imb - Université de Bourgogne <>
Submitted on : Thursday, December 20, 2018 - 9:11:14 AM
Last modification on : Thursday, July 4, 2019 - 3:37:11 PM

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



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