Journal of the Ramanujan Mathematical Society

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On the Proof of The Genus Bound for Enriques–Fano Threefolds


Affiliations
1 Andreas Leopold Knutsen, Department of Mathematics, University of Bergen, Johannes Brunsgate 12, 5008 Bergen, Norway
2 Angelo Felice Lopez, Dipartimento di Matematica, Universita di Roma Tre, Largo San Leonardo Murialdo 1, 00146, Roma, Italy
3 Roberto Munoz, ESCET, Departamento de Matematica Aplicada, Universidad Rey Juan Carlos, 28933 Mostoles (Madrid), Spain
     

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Given an Enriques surface S embedded in 𝕡r with a certain linear system, we show that S is not hyperplane section of any threefold X ⊂ 𝕡r+1 that is not a cone over S. This special case completes the proof of the genus bound for Enriques–Fano threefolds [11, Thm. 1.5].
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  • On the Proof of The Genus Bound for Enriques–Fano Threefolds

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Authors

Andreas Leopold Knutsen
Andreas Leopold Knutsen, Department of Mathematics, University of Bergen, Johannes Brunsgate 12, 5008 Bergen, Norway
Angelo Felice Lopez
Angelo Felice Lopez, Dipartimento di Matematica, Universita di Roma Tre, Largo San Leonardo Murialdo 1, 00146, Roma, Italy
Roberto Munoz
Roberto Munoz, ESCET, Departamento de Matematica Aplicada, Universidad Rey Juan Carlos, 28933 Mostoles (Madrid), Spain

Abstract


Given an Enriques surface S embedded in 𝕡r with a certain linear system, we show that S is not hyperplane section of any threefold X ⊂ 𝕡r+1 that is not a cone over S. This special case completes the proof of the genus bound for Enriques–Fano threefolds [11, Thm. 1.5].