000 03719nam a22004935i 4500
001 978-3-540-30615-3
003 DE-He213
005 20161121231031.0
007 cr nn 008mamaa
008 100301s2006 gw | s |||| 0|eng d
020 _a9783540306153
_9978-3-540-30615-3
024 7 _a10.1007/978-3-540-30615-3
_2doi
050 4 _aQA440-699
072 7 _aPBM
_2bicssc
072 7 _aMAT012000
_2bisacsh
082 0 4 _a516
_223
100 1 _aSernesi, Edoardo.
_eauthor.
245 1 0 _aDeformations of Algebraic Schemes
_h[electronic resource] /
_cby Edoardo Sernesi.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2006.
300 _aXI, 342 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aA Series of Comprehensive Studies in Mathematics,
_x0072-7830 ;
_v334
505 0 _aIntroduction -- Infinitesimal Deformations: Extensions. Locally Trivial Deformations -- Formal Deformation Theory: Obstructions. Extensions of Schemes. Functors of Artin Rings. The Theorem of Schlessinger. The Local Moduli Functors -- Formal Versus Algebraic Deformations. Automorphisms and Prorepresentability -- Examples of Deformation Functors: Affine Schemes. Closed Subschemes. Invertible Sheaves. Morphisms -- Hilbert and Quot Schemes: Castelnuovo-Mumford Regularity. Flatness in the Projective Case. Hilbert Schemes. Quot Schemes. Flag Hilbert Schemes. Examples and Applications. Plane Curves -- Appendices: Flatness. Differentials. Smoothness. Complete Intersections. Functorial Language -- List of Symbols -- Bibliography.
520 _aThe study of small and local deformations of algebraic varieties originates in the classical work of Kodaira and Spencer and its formalization by Grothendieck in the late 1950's. It has become increasingly important in algebraic geometry in every context where variational phenomena come into play, and in classification theory, e.g. the study of the local properties of moduli spaces.Today deformation theory is highly formalized and has ramified widely within mathematics. This self-contained account of deformation theory in classical algebraic geometry (over an algebraically closed field) brings together for the first time some results previously scattered in the literature, with proofs that are relatively little known, yet of everyday relevance to algebraic geometers. Based on Grothendieck's functorial approach it covers formal deformation theory, algebraization, isotriviality, Hilbert schemes, Quot schemes and flag Hilbert schemes. It includes applications to the construction and properties of Severi varieties of families of plane nodal curves, space curves, deformations of quotient singularities, Hilbert schemes of points, local Picard functors, etc. Many examples are provided. Most of the algebraic results needed are proved. The style of exposition is kept at a level amenable to graduate students with an average background in algebraic geometry.
650 0 _aMathematics.
650 0 _aAlgebraic geometry.
650 0 _aCommutative algebra.
650 0 _aCommutative rings.
650 0 _aGeometry.
650 1 4 _aMathematics.
650 2 4 _aGeometry.
650 2 4 _aAlgebraic Geometry.
650 2 4 _aCommutative Rings and Algebras.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540306085
830 0 _aA Series of Comprehensive Studies in Mathematics,
_x0072-7830 ;
_v334
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-540-30615-3
912 _aZDB-2-SMA
950 _aMathematics and Statistics (Springer-11649)
999 _c507583
_d507583