LEADER 03348nam 22005055 450 001 9910163986303321 005 20251230064958.0 024 7 $a10.1007/978-3-319-49763-1 035 $a(CKB)3710000001053495 035 $a(DE-He213)978-3-319-49763-1 035 $a(MiAaPQ)EBC4803140 035 $a(PPN)198871791 035 $a(EXLCZ)993710000001053495 100 $a20170209d2017 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aGeometry Over Nonclosed Fields /$fedited by Fedor Bogomolov, Brendan Hassett, Yuri Tschinkel 205 $a1st ed. 2017. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2017. 215 $a1 online resource (IX, 261 p. 3 illus., 1 illus. in color.) 225 1 $aSimons Symposia,$x2365-9572 311 08$a3-319-49762-6 311 08$a3-319-49763-4 320 $aIncludes bibliographical references. 327 $aPreface -- "On the Kobayashi pseudometric, complex automorphisms and hyperahler manifolds" by Fedor Bogomolov, Ljudmila Kamenova, Steven Lu, and Misha Verbitsky -- "Lines on cubic hypersurfaces over finite fields" by Olivier Debarre, Antonio Laface, and Xavier Roulleau -- "Perverse sheaves of categories and non-rationality" by Andrew Harder, Ludmil Katzarkov, and Yijia Liu -- "Divisor classes and the virtual canonical bundle for genus zero maps" by A. J. de Jong and Jason Starr -- "A stronger derived Torelli theorem for K3 surfaces" by Max Lieblich and Martin Olsson -- "Morphisms to Brauer-Severi varieties, with applications to del Pezzo surfaces" by Christian Liedtke -- "Arithmetic of K3 surfaces" by Anthony Varilly-Alvarado -- "One-dimensional cohomology with finite coefficients and roots of unity" by Yuri G. Zarhin. 330 $aBased on the Simons Symposia held in 2015, the proceedings in this volume focus on rational curves on higher-dimensional algebraic varieties and applications of the theory of curves to arithmetic problems. There has been significant progress in this field with major new results, which have given new impetus to the study of rational curves and spaces of rational curves on K3 surfaces and their higher-dimensional generalizations. One main recent insight the book covers is the idea that the geometry of rational curves is tightly coupled to properties of derived categories of sheaves on K3 surfaces. The implementation of this idea led to proofs of long-standing conjectures concerning birational properties of holomorphic symplectic varieties, which in turn should yield new theorems in arithmetic. This proceedings volume covers these new insights in detail. . 410 0$aSimons Symposia,$x2365-9572 606 $aAlgebraic geometry 606 $aAlgebraic Geometry 615 0$aAlgebraic geometry. 615 14$aAlgebraic Geometry. 676 $a510 702 $aBogomolov$b Fedor$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aHassett$b Brendan$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aTschinkel$b Yuri$4edt$4http://id.loc.gov/vocabulary/relators/edt 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910163986303321 996 $aGeometry Over Nonclosed Fields$91561712 997 $aUNINA