Smoothable del Pezzo surfaces with quotient singularities

By P. Hacking, Yuri Prokhorov. Compositio Mathematica, 2008

135 citations recorded by the source corpus.

Abstract We classify del Pezzo surfaces with quotient singularities and Picard rank one which admit a ℚ-Gorenstein smoothing. These surfaces arise as singular fibres of del Pezzo fibrations in the 3-fold minimal model program and also in moduli problems.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/74ba8cf1c1d5f7bc6329f425bba05fa1ae826d52

How researchers see this paper

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In Algebra and Number Theory

1. Renato Vianna
2. Chi Li
3. Song Sun
4. Cristiano Spotti
5. Y. Odaka

In Geometry and Topology

1. Chi Li
2. Y. Odaka
3. Cristiano Spotti
4. Song Sun
5. Robert J. Berman
6. Chenyang Xu
7. Yuchen Liu
8. Mattias Jonsson

Citations in the corpus

• Infinitely many monotone Lagrangian tori in del Pezzo surfaces (2016, background): “3, we point out that the Markov type I equations have appeared before, in relation to 3-blocks exceptional collections in the del Pezzo surfaces [20] and Q-Gorenstein smoothing of weighted projective spaces to del Pezzo surfaces [16].”
• Special test configurations and $K$-stability of Fano varieties (2011, background): “s often only have semi-log canonical singularities. In particular, they are not always irreducible. We remark that in general special Fano degenerations are not unique. In fact, it is a recent result [HP10] which classifies all the special Fano degenerations of P2. However, even without the uniquenes”
• Compact Moduli Spaces of Del Pezzo Surfaces and K\"ahler-Einstein metrics (2012, methodology): “Clearly we have K(2) Y∞ = 8, and thus we may apply [26].”