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of the canonical divisor of the relative canonical model was
Cartier and the number of exceptional components where this agrees with the same multiple of the canonical divisor of Y is also independent of the choice of Y. When it equals the number of components of Y it was called
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Some basic properties were as follows: The relative canonical model was independent of the choice of resolution. Some integer multiple
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proved that the sheaf in the definition always is finitely generated and therefore that relative canonical models always exist.
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706:. Since that time in the 1970s other mathematicians solved affirmatively the problem of whether they are
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741:(courtesy copy), proceedings of the Angiers 'Journees de Geometrie Algebrique' 1979
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369:{\displaystyle f_{*}\omega _{Y}^{\otimes n}=I_{n}\omega _{X}^{\otimes n}}
702:. The class of varieties that are relative canonical models have
524:{\displaystyle Proj\oplus _{n}f_{*}\omega _{Y}^{\otimes n}\to X}
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define the adjunction sequence to be the sequence of subsheaves
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609:. It was not known whether relative canonical models were
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Because the relative canonical model is independent of
451:{\displaystyle \oplus _{n}f_{*}\omega _{Y}^{\otimes n}}
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659:rather than either the relative canonical model
266:{\displaystyle f_{*}\omega _{Y}^{\otimes n};}
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403:is the higher adjunction ideal. Problem. Is
51:introducing citations to additional sources
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41:Relevant discussion may be found on the
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34:relies largely or entirely on a
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16:Complex manifolds in mathematics
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682:or the canonical blow-up of
186:The precise definition is:
293:{\displaystyle \omega _{X}}
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62:"Relative canonical model"
533:relative canonical model
214:{\displaystyle f:Y\to X}
124:relative canonical model
704:canonical singularities
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396:{\displaystyle I_{n}}
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708:Cohen–Macaulay
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833:Birational geometry
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828:Algebraic geometry
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120:algebraic geometry
838:Complex manifolds
739:Canonical 3-folds
695:{\displaystyle X}
675:{\displaystyle Y}
652:{\displaystyle X}
629:{\displaystyle Y}
595:{\displaystyle r}
572:{\displaystyle X}
557:canonical blow-up
548:{\displaystyle Y}
171:{\displaystyle X}
147:{\displaystyle X}
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58:Find sources:
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36:single source
32:This article
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116:mathematical
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103:October 2021
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764:Mathematics
714:started by
182:Description
822:Categories
776:Arithmetic
722:References
223:resolution
73:newspapers
843:Dimension
800:Chemistry
737:M. Reid,
555:, or the
516:→
508:⊗
499:ω
493:∗
479:⊕
441:⊗
432:ω
426:∗
412:⊕
359:⊗
350:ω
328:⊗
319:ω
313:∗
282:ω
253:⊗
244:ω
238:∗
206:→
156:canonical
118:field of
43:talk page
812:Science
788:Physics
750:Portals
606:crepant
114:In the
87:scholar
710:. The
376:where
134:where
122:, the
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221:is a
130:of a
126:of a
94:JSTOR
80:books
66:news
661:of
638:of
559:of
535:of
273:if
189:If
49:by
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730:^
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336:=
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309:f
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256:n
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200::
197:f
166:X
142:X
105:)
101:(
91:·
84:·
77:·
70:·
53:.
39:.
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