Abstract:
In this paper the following problem is solved: given a singular Fano variety X, find a smooth Enriques surface which is an ample Cartier divisor on X. The results obtained enable one to construct, using singular Fano varieties, examples of threefolds whose hyperplane sections are Enriques surfaces. They can be used in the classification of log-Fano varieties of (Fano) index 1.
\Bibitem{Pro95}
\by Yu.~G.~Prokhorov
\paper On algebraic threefolds whose hyperplane sections are Enriques surfaces
\jour Sb. Math.
\yr 1995
\vol 186
\issue 9
\pages 1341--1352
\mathnet{http://mi.mathnet.ru/eng/sm71}
\crossref{https://doi.org/10.1070/SM1995v186n09ABEH000071}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1360190}
\zmath{https://zbmath.org/?q=an:0868.14020}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1995TX11300007}
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https://www.mathnet.ru/eng/sm71
https://doi.org/10.1070/SM1995v186n09ABEH000071
https://www.mathnet.ru/eng/sm/v186/i9/p113
This publication is cited in the following 8 articles:
Lee N.-H., “Calabi-Yau Double Coverings of Fano-Enriques Threefolds”, Proc. Edinb. Math. Soc., 62:1 (2019), 107–114
Karzhemanov I., “On Some Fano-Enriques Threefolds”, Adv. Geom., 11:1 (2011), 117–129
I. V. Karzhemanov, “On Fano threefolds with canonical Gorenstein singularities”, Sb. Math., 200:8 (2009), 1215–1246
I. A. Cheltsov, “Rationality of an Enriques–Fano threefold of genus five”, Izv. Math., 68:3 (2004), 607–618
Luis Giraldo, Angelo Lopez, Roberto Muñoz, “On the existence of Enriques-Fano threefolds of index greater than one”, J. Algebraic Geom., 13:1 (2003), 143
F. Ambro, “Ladders on Fano varieties”, Journal of Mathematical Sciences (New York), 94:1 (1999), 1126
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