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020 _a9783319497631
_9978-3-319-49763-1
024 7 _a10.1007/978-3-319-49763-1
_2doi
040 _aISI Library, Kolkata
050 4 _aQA564-609
072 7 _aPBMW
_2bicssc
072 7 _aMAT012010
_2bisacsh
072 7 _aPBMW
_2thema
082 0 4 _a516.35
_223
245 1 0 _aGeometry Over Nonclosed Fields
_h[electronic resource] /
_cedited by Fedor Bogomolov, Brendan Hassett, Yuri Tschinkel.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2017.
300 _aIX, 261 p. 3 illus., 1 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSimons Symposia,
_x2365-9564
505 0 _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.
520 _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. .
650 0 _aGeometry, algebraic.
650 1 4 _aAlgebraic Geometry.
_0http://scigraph.springernature.com/things/product-market-codes/M11019
700 1 _aBogomolov, Fedor.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
700 1 _aHassett, Brendan.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
700 1 _aTschinkel, Yuri.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783319842356
776 0 8 _iPrinted edition:
_z9783319497624
776 0 8 _iPrinted edition:
_z9783319497648
830 0 _aSimons Symposia,
_x2365-9564
856 4 0 _uhttps://doi.org/10.1007/978-3-319-49763-1
912 _aZDB-2-SMA
942 _cEB
950 _aMathematics and Statistics (Springer-11649)
999 _c427099
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