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| Sernesi E. — Topics of families of projective schemes |
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| Предметный указатель |
(TF)-finite graded module section 1 page 8
Action, free and transitive section B page 5
Arithmetically Cohen — Macaulay (a. CM.) scheme section 9 page 8
Associated point section 2 page 5
Base-change section 2 page 2 section section
Bertini’s theorem section 11 page 16 section
Brill — Noethermap section 11 page 6
Bundle grassmannian section 1 page 7
Bundle projective section 1 page 7
Bundle tautological section 1 page 5 section
Bundle universal quotient section 1 page 3
Characteristic map of a family section 8 page 2
Characteristic of a formal element section B page 4
Chow point section 7 page 12
Classifying morphism ( or map) section 7 page 3
Clifford’s theorem section 11 page 19
Complete intersection section 8 page 3 section section section section section
Complete intersection, local section 4 page 8
Component, connected section 2 page 12 section
Component, pathological section 11 page 14
Component, regular section 11 page 13
Component, superabundant section 11 page 13
Cone, quadric section 10 page 9
Conic(s) section 2 page 7 section section section
Conicalinfinitesimal deformation section 9 page 1
Connected component section 2 page 12 section
Connected curve section 11 page 18
Connected fibre section 5 page 7 section
Connected scheme section 5 pages 2—4 section section
Constructive subset section 2 page 7
Coupie(s) section 1 page 3
Coupie(s), isomorphism of section B page 8
Coupie(s), semiuniversal section B page 8
Coupie(s), universal section B page 8
Coupie(s), versal section B page 8
Covering section 1 page 2 section section
Cubic surface section 9 page 7 section
Curve(s), branch of section 11 page 2
Curve(s), canonical section 11 page 7
Curve(s), connected section 11 page 18
Curve(s), intersecting quasi-transversally section 11 page 10
Curve(s), non-degenerate section 11 page 5
Curve(s), non-special section 11 page 6
Curve(s), piane section 11 page 2
Curve(s), quintic section 11 page 16
Curve(s), unobstructed section 9 page 7 section section section
Deformation(s), conical section 9 page 1
Deformation(s), embedded section 4 page 4
Deformation(s), first order see “First order deformation”
Deformation(s), flat family of section 2 page 4
Deformation(s), infinitesimal see “Infinitesimal (family of) deformations”
Deformation(s), local family of section 2 page 4
Deformation(s), trivial section 2 page 8
Derivation(s) section A page 5 section section section
Differential(s) of a morphism section 2 page 13 section
Differential(s) of functors section B page 3
Differential(s), sheaf of section 9 page 6 section
Discrete valuation ring (DVR) section 2 page 5 section section
Double point (ordinary) section 11 page 10 section
Dual numbers, algebra of section A page 6
Dual projective space section 1 page 5
Element, formal section B page 1
Embedded deformation section 4 page 4
Embedded point section 5 page 5
Embedding, closed section 1 page 6 1
Embedding, regular section 4 page 8
Etale morphism of rings section A page 1
Etale morphism of schemes section 2 page 8
Euler sequence section 11 page 1
Exact sequence of normal bundles section 4 page 9
Exact sequence of normal sheaves section 4 page 9
Exact sequence, Euler section 11 page 1
Extension section A page 5
Extension, trivial section A page 5
Faithfully flat, algebra section 2 page 1
Faithfully flat, module section 2 page 1
Family, complete section 7 page 12
Family, effectively parametrized section 7 page 12
Family, flat section 2 page 4
Family, local section 2 page 4
Family, smooth section 2 page 9
Family, universal section 7 page 3 10 10 10
First order deformation section 8 page 1
First order deformation of X in Y section 4 page 6
Flag of closed subschemes section 10 page 4
Flag — Hilbert functor section 10 page 1
Flag — Hilbert scheme section 10 page 1
Flat algebra section 2 page 1
Flat family section 2 page 4
Flat family of closed subschemes section 2 page 8
Flat module section 2 page 1
Flat morphism of rings section 2 page 1
Flat morphism of schemes section 2 page 4
Flat sheaf section 2 page 3
Formal element section B page 1
Formally etale morphism of rings section A page 1
Formally etale morphism of schemes section 2 page 8
Formally smooth morphism of rings section A page 1
Formally smooth morphism of schemes section 2 page 8
Functor of (embedded) infinitesimal deformations of X in Y section 4 page 4
Functor of Artin rings section B page 1
Functor of conical infinitesimal deformations section 9 page 1
Functor of finite dimension section B page 20
Functor, connected section B page 20
Functor, Grassmann section 1 page 3
Functor, Hilbert see “Hilbert functor”
Functor, homogeneous section B page 20
Functor, left exact section 8 page 2
Functor, local Hubert section 8 page 1
Functor, prorepresentable section B page 1
Functor, represenlable section 1 page 1
Functor, semi-homogeneous section B page 20
Functor, which is a sheaf (in the Zariski topology) section 1 page 1
Generic point section 2 page 5
Genus section 11 page 1
Genus, arithmetic section 11 page 9
Graph section 1 page 7 section
Grassmanman section 1 page 5
Grassmanman, bundle section 1 page 7
Grassmann functor section 1 page 3
Hilbert functor section 7 page 8
Hilbert functor of a fixed subscheme section 10 page 5
Hilbert functor of closed subschemes of  containing a fixed subscheme section 10 page 6
Hilbert functor, local section 8 page 1
Hilbert scheme section 7 page 2
Hilbert scheme of a fixed subscheme section 10 page 5
Hilbert scheme of closed subschemes of containing a fixed subscheme section 10 page 7
Hilbert — Burch theorem section 9 page 11
Incidence relation section 1 page 8
Infinitesimal deformation section 2 page 4
Infinitesimal deformation of X in Y section 2 page 8
| Koszui relation(s) section 4 page 9 8
Koszui relation(s), sheaf of section 8 page 9
Koszul complex section 4 page 4 section section
Left exact functor section B page 2
Less obstructed algebra section A page 23
Linear system section 7 page 9 7
Local complete intersection section 4 page 8
Local criterion of flatness section 2 page 3
Local family of closed subschemes section 2 page 8
Local family of deformations section 2 page 4
Local Hilbert functor section 8 page 1
Macaulay’s theorem section 9 page 7
Maximal rank, scheme of section 9 page 9 (see also “Curve of maximal rank”)
monodromy section 8 page 8
morphism of section 8 page 8
Morphism of couples section B page 8
Morphism, closed section 5 page 4
Morphism, etale see “Etalemorphism”
Morphism, flat see “Flat morphism”
Morphism, formally etale see “Formally etale morphism”
Morphism, formally smooth see “Formally smooth morphism”
Morphism, obstructed section A page 23
Morphism, smooth see “Smooth morphism”
Morphism, unobstructed section A page 23
Nilpotent ideal section 2 page 3 section
Node section 11 page 10
Noether’s Normalization Lemma section 2 page 6
Non-degenerate curve section 11 page 5
Non-special curve section 11 page 6
Normal bundle section 4 page 8
Normal sheaf section 4 page 8
Obstructed algebra section A page 17
Obstructed morphism section A page 23
Obstructed scheme section 8 page 1
Obstructed scheme, example of an section 8 page 12
Obstruction space for  section 8 page 12
Obstruction space for  section 9 page 2
Obstruction space for a functor section B page 11
Obstruction space of a closed subscheme of section 8 page 9
Obstruction space of an algebra section A page 18
Obstruction space of X in Y section 10 page 8
Obstruction(s) to lift a morphism section A page 20
Obstruction(s), module of section 4 page 9
Obstruction(s), sheaf of section 4 page 11
Parametrized flag section 10 page 4
Parametrized scheme section 7 page 7
Parametrizing, point section 7 page 7 section
Pathological component section 11 page 14
Picard group section 7 page 11
Plucker morphism (embedding) section 1 page 6
Point, associated section 2 page 5
Point, Chow section 7 page 12
Point, embedded section 5 page 5
Point, generic section 2 page 15
Principal homogeneous space section 8 page 5
Principal parts, sheaf of section 11 page 8
Projective bundle section 1 page 7
Projectively normal curve section 9 page 9
Prorepresentable functor section B page 1
Pullback of an extension section A page 6
Pushout of an extension section A page 6
Quadric cone section 10 page 9 section
Quadric surface section 2 page 7 section section section section section
Quartic surface section 11 page 15 section section
Quasi-transversally, curves intersecting section 11 page 10
Regular component section 11 page 13
Regular embedding section 4 page 8
Regular sequence section 4 page 3 section section
Regularly embedded closed subscheme section 4 page 8
Relation(s), incidence section 1 page 8
Relation(s), Koszul (or trivial) section 4 page 9 section
Relation(s), Koszul (or trivial), sheaf of section 8 page 9
Relation(s), sheaf of section 9 page 2
Relative dimension section 2 page 5 section
Representable functor section 1 page 1
Ruled surface section 11 page 9
Saturated homogeneous ideal section 1 page 9
Schlessinger’s theorem section B page 14
Schubert cycle section 7 page 12
Section section 7 page 10 section
Semi continuity theorem section 3 page 10
Semi-homogeneous functor section B page 20
Semiuniversal couple section B page 8
Semiuniversal element section B page 8
Sheaf (in the Zanski topology) section 1 page 1
Sheaf of Koszul relations section 8 page 9
Sheaf of relations section 9 page 2
Sheaf, m-regular section 1 page 12
Smooth functor section B page 5
Smooth morphism of functors section B page 5
Smooth morphism of rings section A page 1
Smooth morphism of schemes section 2 page 8
Stratification section 1 page 9
Stratification, flattening section 6 page 1
Stratum(a) section 1 page 9
Subfunctor, closed section 1 page 2
Subfunctor, of section 9 page 4
Subfunctor, open section 1 page 2
Superabundant component section 11 page 13
Surface, cubic section 9 page 7 section
Surface, quadric section 2 page 7 section section
Surface, quartic section 11 page 15 11 11
Surface, ruled section 11 page 9
Tangent sheaf section 11 page 1
Tangent space of  section 4 page 6
Tangent space of  section 8 page 1
Tangent space of a functor section B page 3
Tangent space of a local k-algebra section A page 17
Tautological bundle section 1 page 5
Theorem, Bertini’s section 11 page 16 section
Theorem, Clifford’s section 11 page 19
Theorem, Hilbert — Burch section 9 page 11
Theorem, Macauiay’s section 9 page 7
Theorem, Schiessinger’s section 8 page 14
Theorem, Semicontinuity section 3 page 10
Total space section 2 page 4
Trivial relation(s) section 4 page 9
Universal couple section B page 8
Universal family section 7 page 3 section section section
Universal formal element section B page 2
Universal property of  section 1 page 5
Universal property of  section 7 page 3
Universal property of o(R) section A page 21
Universal quotient bundle section 1 page 3
Unobstructed morphism section A page 23
Unobstructed scheme section 8 page 1
Upper semi-continuous function section 1 page 10 section
Valuative criterion of properness section 7 page 6
Versal couple section B page 8
Versal couple, formal element section B page 8
Zariski tangent space see “Tangent space”
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