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2016, Monographs and research notes in mathematics, ISBN 9781482251593, xxi, 504
Cremona Groups and the Icosahedron focuses on the Cremona groups of ranks 2 and 3 and describes the beautiful appearances of the icosahedral group A5 in them.... 
Icosahedra | Automorphic forms | Geometry, Algebraic | Geometry | Algebra | Number Theory
Book
American journal of mathematics, ISSN 0002-9327, 2016, Volume 138, Issue 2, pp. 403 - 418
Assuming the Borisov-Alexeev-Borisov conjecture, we prove that there is a constant J = J(n) such that for any rationally connected variety X of dimension n and... 
Cremona transformations | Jordan algebras | Geometry, Algebraic | EXISTENCE | MATHEMATICS | FINITE SUBGROUPS | SINGULARITIES | DEGENERATIONS | RATIONAL CONNECTEDNESS | CONJECTURE | Analysis | Group theory | Geometry | Algebra
Journal Article
Japanese journal of mathematics, ISSN 1861-3624, 2018, Volume 13, Issue 1, pp. 109 - 185
We discuss various results on Hilbert schemes of lines and conics and automorphism groups of smooth Fano threefolds of Picard rank 1. Besides a general review... 
14J45 | line | 14J50 | Mathematics | History of Mathematical Sciences | derived category | 14C05 | 14J30 | Hilbert scheme | automorphism group | Mathematics, general | conic | Fano variety | PROPERTY | SECTIONS | CLASSIFICATION | SUBGROUPS | CATEGORIES | CREMONA GROUP | MATHEMATICS | JORDAN CONSTANT | FAMILIES | MANIFOLDS | VECTOR-BUNDLES | Algebra | Mathematics - Algebraic Geometry
Journal Article
Rendiconti del Circolo matematico di Palermo, ISSN 1973-4409, 2016, Volume 66, Issue 2, pp. 161 - 194
... · Michal Farnik 2 · Alex Küronya 3 · Victor Lozovanu 4 · Joaquim Roé 5 · Constantin Shramov 6,7 Received: 5 February 2016 / Accepted: 22 October 2016 / Published... 
Newton-Okounkov body | Linear system | Valuation | Algebraic geometry | Valuative tree
Journal Article
Transformation Groups, ISSN 1083-4362, 6/2012, Volume 17, Issue 2, pp. 303 - 350
We study the action of the Klein simple group PSL2( $ {\mathbb{F}_7} $ ) consisting of 168 elements on two rational threefolds: the three-dimensional... 
Topological Groups, Lie Groups | Mathematics | Algebra | MATHEMATICS | ABELIAN SURFACES | FINITE SUBGROUPS | ALGEBRA | KAHLER-EINSTEIN METRICS | MODULI | 3-FOLDS
Journal Article
2016, Monographs and research notes in mathematics, ISBN 9781482251593, 527
Cremona Groups and the Icosahedron focuses on the Cremona groups of ranks 2 and 3 and describes the beautiful appearances of the icosahedral group A5 in them.... 
Geometry | Algebra | Number Theory | Icosahedra | Automorphic forms | Geometry, Algebraic
eBook
Selecta Mathematica, ISSN 1022-1824, 12/2019, Volume 25, Issue 5, pp. 1 - 68
... Ivan Cheltsov 1,2 · Constantin Shramov 2,3 Published online: 13 November 2019 © Springer Nature Switzerland AG 2019 Abstract We classify finite groups G in PGL 4 (C... 
Mathematics, general | 14J50 | Mathematics | 14N05 | MATHEMATICS | FIELDS | MATHEMATICS, APPLIED | BUNDLES | VARIETIES | CLASSIFICATION | EMBEDDINGS | CURVES | WEAK FANO THREEFOLDS | CREMONA GROUP | SURFACES
Journal Article
Compositio mathematica, ISSN 0010-437X, 12/2014, Volume 150, Issue 12, pp. 2054 - 2072
...COMPOSITIO MATHEMATICA Jordan property for groups of birational selfmaps Yuri Prokhorov and Constantin Shramov Compositio Math. 150 (2014), 20542072. http... 
birational automorphisms | divisor class group | Jordan group | minimal model program | MATHEMATICS | VARIETIES | AUTOMORPHISM-GROUPS | GENERAL TYPE | Algebraic group theory | Algebra | Mathematical analysis | Automorphisms | Subgroups | Group theory | Mathematics - Algebraic Geometry
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 03/2014, Volume 366, Issue 3, pp. 1289 - 1331
We propose a new method to study birational maps between Fano varieties based on multiplier ideal sheaves. Using this method, we prove equivariant birational... 
Linear systems | Morphisms | Geometry | Tangents | Homomorphisms | Mathematical theorems | Algebra | Hyperplanes | Rational numbers | Automorphisms | SPACE | MATHEMATICS | DEL PEZZO SURFACES | PLANE | 6 LINES | KAHLER-EINSTEIN METRICS | BIRATIONAL GEOMETRY | QUOTIENT SINGULARITIES | 3-FOLDS
Journal Article
PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS, ISSN 0081-5438, 11/2019, Volume 307, Issue 1, pp. 198 - 209
We show that smooth well-formed weighted complete intersections have finite automorphism groups, with several obvious exceptions. 
MATHEMATICS | POLARIZED MANIFOLDS | MATHEMATICS, APPLIED
Journal Article
Proceedings of the Steklov Institute of Mathematics, ISSN 0081-5438, 8/2015, Volume 290, Issue 1, pp. 91 - 102
... in Grassmannians Victor V. Przyjalkowski a and Constantin A. Shramov a Received March 15, 2015 Abstract— In 1997 Batyrev, Ciocan-Fontanine, Kim, and van Straten suggested... 
Mathematics, general | Mathematics | MATHEMATICS | TORIC DEGENERATIONS | MATHEMATICS, APPLIED | MIRROR SYMMETRY
Journal Article
Journal of algebraic geometry, ISSN 1534-7486, 2018, Volume 28, Issue 2, pp. 201 - 243
We study the rationality problem for nodal quartic double solids. In particular, we prove that nodal quartic double solids with at most six singular points are... 
MATHEMATICS | VARIETIES
Journal Article
European Journal of Mathematics, ISSN 2199-675X, 9/2018, Volume 4, Issue 3, pp. 845 - 858
... Ivan Cheltsov 1,2 · Jihun Park 3,4 · Constantin Shramov 2,5 Received: 17 September 2017 / Revised: 16 March 2018 / Accepted: 22 March 2018 / Published online: 13... 
32Q26 | 14J45 | Log terminal singularity | Log Fano variety | Purely log terminal blow-up | Algebraic Geometry | Mathematics | Alpha-invariant of Tian | 14E05
Journal Article
Geometry and Topology, ISSN 1465-3060, 2011, Volume 15, Issue 4, pp. 1843 - 1882
We study exceptional quotient singularities. In particular, we prove an exceptionality criterion in terms of the alpha-invariant of Tian, and utilize it to... 
Quotient singularities | Group | Kähler-Einstein metric | Log canonical threshold | Alpha invariant | Fano | MATHEMATICS | INVARIANTS | KAHLER-EINSTEIN METRICS
Journal Article
Experimental Mathematics, ISSN 1058-6458, 07/2013, Volume 22, Issue 3, pp. 313 - 326
We study del Pezzo surfaces that are quasismooth and well-formed weighted hypersurfaces. In particular, we find all such surfaces whose α-invariant of Tian is... 
del Pezzo surface | Kahler-Einstein metric | Fano variety | alpha-invariant of Tian | Alpha-invariant of Tian | Del Pezzo surface | EXISTENCE | MATHEMATICS | KAHLER-EINSTEIN METRICS
Journal Article
Proceedings of the Steklov Institute of Mathematics, ISSN 0081-5438, 8/2016, Volume 294, Issue 1, pp. 154 - 175
... a and Constantin A. Shramov a Received April 1, 2016 Abstract— We classify nodal Fano threefolds that are double covers of smooth quadrics branched over intersections... 
Mathematics, general | Mathematics | FANO THREEFOLDS | MATHEMATICS | VARIETIES | DOUBLE SOLIDS | MATHEMATICS, APPLIED | BIRATIONAL AUTOMORPHISMS
Journal Article
European Journal of Mathematics, ISSN 2199-675X, 3/2016, Volume 2, Issue 1, pp. 96 - 119
... , 3 · Victor Przyjalkowski 2 , 3 · Constantin Shramov 2 , 3 Received: 8 September 2015 / Accepted: 7 November 2015 / Published online: 30 November 2015 © Springer... 
14E08 | 14E07 | 14J45 | Rationality | Quartic surface | Algebraic Geometry | Fano threefold | Mathematics | 14E05 | Icosahedron
Journal Article
Mathematical Research Letters, ISSN 1073-2780, 2011, Volume 18, Issue 6, pp. 1121 - 1139
We classify six-dimensional exceptional quotient singularities and show that seven-dimensional exceptional quotient singularities do not exist. Inter alia we... 
MATHEMATICS
Journal Article
European Journal of Mathematics, ISSN 2199-675X, 3/2016, Volume 2, Issue 1, pp. 1 - 8
... Mangolte 4 · Constantin Shramov 2 , 5 · Damiano Testa 6 Published online: 14 December 2015 © Springer International Publishing AG 2015 This volume contains 20 papers... 
Algebraic Geometry | Mathematics
Journal Article
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