LEADER 03350nam 22005055 450 001 9910506387803321 005 20251113203654.0 010 $a3-030-75421-9 024 7 $a10.1007/978-3-030-75421-1 035 $a(CKB)4950000000280048 035 $a(MiAaPQ)EBC6787294 035 $a(Au-PeEL)EBL6787294 035 $a(OCoLC)1281969980 035 $a(PPN)258296968 035 $a(DE-He213)978-3-030-75421-1 035 $a(EXLCZ)994950000000280048 100 $a20211019d2021 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aRationality of Varieties /$fedited by Gavril Farkas, Gerard van der Geer, Mingmin Shen, Lenny Taelman 205 $a1st ed. 2021. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2021. 215 $a1 online resource (440 pages) 225 1 $aProgress in Mathematics,$x2296-505X ;$v342 311 08$a3-030-75420-0 320 $aIncludes bibliographical references. 327 $aRationality of Fano threefolds of degree 18 over nonclosed fields -- A categorical invariant for geometrically rational surfaces with a conic bundle structure -- Vanishing cycles under base change and the integral Hodge conjecture -- Explicit rationality of some Fano fourfolds -- Unirationality of certain universal families of cubic fourfolds -- Rational curves and MBM classes on hyperk ähler manifolds: a survey -- Marked and labelled Gushel-Mukai fourfolds -- The Igusa quartic and the Prym map. (I) Some Rationality results -- Rationality of Mukai varieties over non-closed fields -- A refinement of the motivic volume, and specialization of birational types -- On the image of the second ell-adic Bloch map -- Supersingular irreducible symplectic varieties -- On the geometry of Fano threefold hypersurfaces -- Symbols and equivariant birational geometry in small dimensions. 330 $aThis book provides an overview of the latest progress on rationality questions in algebraic geometry. It discusses new developments such as universal triviality of the Chow group of zero cycles, various aspects of stable birationality, cubic and Fano fourfolds, rationality of moduli spaces and birational invariants of group actions on varieties, contributed by the foremost experts in their fields. The question of whether an algebraic variety can be parametrized by rational functions of as many variables as its dimension has a long history and played an important role in the history of algebraic geometry. Recent developments in algebraic geometry have made this question again a focal point of research and formed the impetus to organize a conference in the series of conferences on the island of Schiermonnikoog. The book follows in the tradition of earlier volumes, which originated from conferences on the islands Texel and Schiermonnikoog. 410 0$aProgress in Mathematics,$x2296-505X ;$v342 606 $aAlgebraic geometry 606 $aAlgebraic Geometry 615 0$aAlgebraic geometry. 615 14$aAlgebraic Geometry. 676 $a516.35 702 $aFarkas$b Gavril 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910506387803321 996 $aRationality of varieties$92899032 997 $aUNINA