## Surveys in Geometry and Number Theory: Reports on Contemporary Russian Mathematics, Volume 13The focus of this book is the continuing strength of pure mathematics in Russia after the post-Soviet diaspora. The authors are eight young specialists who are associated with strong research groups in Moscow and St. Petersburg in the fields of algebraic geometry and number theory. Their articles are based on lecture courses given at British universities. The articles are mainly surveys of the recent work of the research groups and contain a substantial number of original results. Topics covered are embeddings and projective duals of homogeneous spaces, formal groups, mirror duality, del Pezzo fibrations, Diophantine approximation and geometric quantization. The authors are I. Arzhantsev, M. Bondarko, V. Golyshev, M. Grinenko, N. Moshchevitin, E. Tevelev, D. Timashev and N. Tyurin. Mathematical researchers and graduate students in algebraic geometry and number theory worldwide will find this book of great interest. |

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aﬃne embeddings aﬃnely closed algebraic geometry algebraic group algebraic varieties automorphisms Bhw,rS birational Bohr-Sommerfeld Borel subgroup canonical classiﬁcation coloured complex compute cone conjecture consider corresponding curve D–module decomposition deﬁned Deﬁnition del Pezzo surfaces denote diﬀerent diﬀerential dimension divisor dual variety equation Example exists Fano Fano variety ﬁbres ﬁnite ﬁrst ﬁxed formal group law formula G-module G-orbit G-stable G-variety group G Hamiltonian vector ﬁeld hence highest weight homogeneous spaces homomorphism horospherical hypersurface integral intersection invariant algebras irreducible isomorphic Lagrangian lattice Lemma line bundle linear Math matrix moduli space monoid Mori ﬁbration morphism multiplication non-singular orbit Pezzo surfaces polynomial projective space projective variety Proof Proposition quantization quantum rational representation result satisﬁes semisimple simple singular smooth function spherical varieties subalgebra subset subspace subvariety Suppose surfaces of degree symplectic manifold tangent Theorem theory torus unipotent