Five embeddings of one simple group
Ivan Cheltsov,Constantin Shramov +1 more
TLDR
In this paper, the authors proposed a new method to study Birational maps between Fano varieties based on multiplier ideal sheaves and proved equivariant Birational rigidity of four Fano threefolds acted on by the group A6.Abstract:
We propose a new method to study birational maps between Fano varieties based on multiplier ideal sheaves. Using this method, we prove equivariant birational rigidity of four Fano threefolds acted on by the group A6. As an application, we obtain that Bir(P 3 ) has at least five non-conjugate subgroups isomorphic to A6.read more
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Three embeddings of the Klein simple group into the Cremona group of rank three
Ivan Cheltsov,Constantin Shramov +1 more
TL;DR: In this paper, the action of the Klein simple group PSL2(potion $ {\mathbb{F}_7} $ fixme ) consisting of 168 elements on two rational three-folds is studied.
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Three embeddings of the Klein simple group into the Cremona group of rank three
Ivan Cheltsov,Constantin Shramov +1 more
TL;DR: In this paper, the action of the Klein simple group G consisting of 168 elements on two rational three-folds is studied and a smooth Fano threefold X of anticanonical degree 22 and index 1 is constructed.
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Quartic double solids with icosahedral symmetry
Ivan Cheltsov,Ivan Cheltsov,Victor Przyjalkowski,Victor Przyjalkowski,Constantin Shramov,Constantin Shramov +5 more
TL;DR: In this article, the authors studied quartic double solids admitting icosahedral symmetry and showed that these solids admit four-dimensional icosahedra and four-fold symmetry.
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G-Fano threefolds, II
TL;DR: In this paper, the authors classify Fano threefold with only Gorenstein terminal singularities and Picard number greater than 1 satisfying an additional assumption that the invariant part of the Weil divisor class group is of rank 1 with respect to an action of some group.
References
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The MAGMA algebra system I: the user language
TL;DR: MAGMA as mentioned in this paper is a new system for computational algebra, and the MAGMA language can be used to construct constructors for structures, maps, and sets, as well as sets themselves.
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Geometry of algebraic curves
TL;DR: This chapter discusses Brill-Noether theory on a moving curve, and some applications of that theory in elementary deformation theory and in tautological classes.
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Compact Complex Surfaces
TL;DR: In this article, the authors describe the topology and algebraic properties of complex surfaces, including the following properties: 1. The Projective Plane, 2. The Jacobian Fibration, 3. Hodge Theory on Surfaces, 4. Inequahties for Hodge Numbers, 5. Holomorphic Vector Bundles, Serre Duality and Riemann-Roch Theorem.