000 02604nam a22004455i 4500
001 978-1-4419-1596-2
003 DE-He213
005 20140220084506.0
007 cr nn 008mamaa
008 100301s2010 xxu| s |||| 0|eng d
020 _a9781441915962
_9978-1-4419-1596-2
024 7 _a10.1007/978-1-4419-1596-2
_2doi
050 4 _aQA564-609
072 7 _aPBMW
_2bicssc
072 7 _aMAT012010
_2bisacsh
082 0 4 _a516.35
_223
100 1 _aHartshorne, Robin.
_eauthor.
245 1 0 _aDeformation Theory
_h[electronic resource] /
_cby Robin Hartshorne.
250 _a1.
264 1 _aNew York, NY :
_bSpringer New York,
_c2010.
300 _aVIII, 236p. 19 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aGraduate Texts in Mathematics,
_x0072-5285 ;
_v257
505 0 _aFirst-Order Deformations -- Higher-Order Deformations -- Formal Moduli -- Global Questions.
520 _aThe basic problem of deformation theory in algebraic geometry involves watching a small deformation of one member of a family of objects, such as varieties, or subschemes in a fixed space, or vector bundles on a fixed scheme. In this new book, Robin Hartshorne studies first what happens over small infinitesimal deformations, and then gradually builds up to more global situations, using methods pioneered by Kodaira and Spencer in the complex analytic case, and adapted and expanded in algebraic geometry by Grothendieck. Topics include: * deformations over the dual numbers; * smoothness and the infinitesimal lifting property; * Zariski tangent space and obstructions to deformation problems; * pro-representable functors of Schlessinger; * infinitesimal study of moduli spaces such as the Hilbert scheme, Picard scheme, moduli of curves, and moduli of stable vector bundles. The author includes numerous exercises, as well as important examples illustrating various aspects of the theory. This text is based on a graduate course taught by the author at the University of California, Berkeley.
650 0 _aMathematics.
650 0 _aGeometry, algebraic.
650 1 4 _aMathematics.
650 2 4 _aAlgebraic Geometry.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781441915955
830 0 _aGraduate Texts in Mathematics,
_x0072-5285 ;
_v257
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4419-1596-2
912 _aZDB-2-SMA
999 _c110432
_d110432