Moscow Mathematical Journal

Volume 18, Issue 4, October–December 2018 pp. 721–737.

Standard Models of Degree 1 del Pezzo Fibrations

Authors: Konstantin Loginov (1)
Author institution:(1) Laboratory of Algebraic Geometry, Faculty of Mathematics, National Research University Higher School of Economics, 119048 Moscow, Usacheva str., 6

Summary:

We construct a standard birational model (a model that has Gorenstein canonical singularities) for the three-dimensional del Pezzo fibrations π: X→C of degree 1 and relative Picard number 1. We also embed the standard model into the relative weighted projective space ℙ_C(1,1,2,3). Our construction works in the G-equivariant category where G is a finite group.

2010 Math. Subj. Class. 14E07.

Keywords: Minimal model program, del Pezzo fibrations, standard model.

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