Finite Subgroups of the Plane Cremona Group

By Igor Dolgachev, V. Iskovskikh. 2006

287 citations recorded by the source corpus.

This paper completes the classic and modern results on classification of conjugacy classes of finite subgroups of the group of birational automorphisms of the complex projective plane.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/86b34f9b934de2dcc3806fb8adbae1e351cb8bb8

How researchers see this paper

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In Discrete Mathematics and Combinatorics

1. Ivan Cheltsov
2. Ingrid Bauer
3. F. Catanese
4. Yuri Prokhorov
5. Constantin Shramov
6. Igor Dolgachev
7. V. Popov

In Geometry and Topology

1. Ingrid Bauer
2. Yuri Prokhorov
3. F. Catanese
4. Ralph Blumenhagen
5. Constantin Shramov
6. Thomas W. Grimm
7. T. Weigand
8. Ivan Cheltsov

In Mathematical Physics

1. Ingrid Bauer
2. Thomas W. Grimm
3. F. Catanese
4. T. Weigand
5. Ralph Blumenhagen
6. Yuri Prokhorov
7. Ivan Cheltsov
8. Volker Braun

Citations in the corpus

• Reflection groups in algebraic geometry (2006, background): “rtial classification of finite groups G which can be realized as groups of automorphisms of some rational surface was given by S. Kantor (for a complete classification and the history of the problem see [33]). Example 5.4. Let X be a Del Pezzo surface with N + 1 = rank SX. We refer to the number 9 −N a”
• GUTs in Type IIB Orientifold Compactifications (2008, background): “In this case, 6 of the points necessarily lie on a conic [81], so this involution cannot be realised on a del Pezzo surface.”
• Jordan property for Cremona groups (2012, background): “The group Cr2(k) and its subgroups have been a subject of research for many years (see [8], [9], [29] and references therein).”
• Topics in classical algebraic geometry (2006, background): “We intentionally omitted the discussion of finite subgroups of the Cremona group Cr(2), the modern account of this classification and the history can be found in [99].”
• Classical Algebraic Geometry: A Modern View (2012, background): “1 This corrects the mistake in [189], where the equation defines a singular surface.”
• Burniat surfaces I: fundamental groups and moduli of primary Burniat surfaces (2009, methodology): “remona group Crn(k) is the group of birational transformations of Pn k, or equivalently the group of k-automorphisms of the field k(x1,...,xn). Finite subgroups of Cr2(C) are completely classified (see [DI09] and references therein). In contrast, subgroups of Crn(k) for n ≥ 3 are not studied well (cf.”
• Log Canonical Thresholds of Del Pezzo Surfaces (2007, background): “We did not prove that groups in Example 5.5 and Lemmata 5.6, 5.7 and 5.8 act on X in such a way that the G-invariant subgroup in Pic(X) is Z. But the latter is well known (see [ DoI ]).”