000 | 03719nam a22004935i 4500 | ||
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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 |
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024 | 7 |
_a10.1007/978-3-540-30615-3 _2doi |
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050 | 4 | _aQA440-699 | |
072 | 7 |
_aPBM _2bicssc |
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072 | 7 |
_aMAT012000 _2bisacsh |
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082 | 0 | 4 |
_a516 _223 |
100 | 1 |
_aSernesi, Edoardo. _eauthor. |
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245 | 1 | 0 |
_aDeformations of Algebraic Schemes _h[electronic resource] / _cby Edoardo Sernesi. |
264 | 1 |
_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2006. |
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300 |
_aXI, 342 p. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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338 |
_aonline resource _bcr _2rdacarrier |
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347 |
_atext file _bPDF _2rda |
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490 | 1 |
_aA Series of Comprehensive Studies in Mathematics, _x0072-7830 ; _v334 |
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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 |