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177:. For three-dimensional algebraic varieties, Ein and Lazarsfeld in 1993 proved the first part of the Fujita conjecture, i.e. that
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211:(1993), "Global generation of pluricanonical and adjoint linear series on smooth projective threefolds.",
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Siu, Yum-Tong (1996), "The Fujita conjecture and the extension theorem of Ohsawa-Takegoshi",
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Fujita, Takao (1987), "On polarized manifolds whose adjoint bundles are not semipositive",
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157:(and its complex analytic variant). Fujita conjecture provides an explicit bound on
337:"A tight closure proof of Fujita's freeness conjecture for very ample line bundles"
250:, Adv. Stud. Pure Math., vol. 10, North-Holland, Amsterdam, pp. 167–178,
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32:. It is named after Takao Fujita, who formulated it in 1985.
314:, World Sci. Publ., River Edge, NJ, pp. 577–592,
40:
In complex geometry, the conjecture states that for a
281:Helmke, Stefan (1997), "On Fujita's conjecture",
173:For surfaces the Fujita conjecture follows from
8:
363:
312:Geometric complex analysis (Hayama, 1995)
224:
7:
14:
226:10.1090/S0894-0347-1993-1207013-5
247:Algebraic geometry, Sendai, 1985
24:is a problem in the theories of
181:≥4 implies global generation.
153:is very ample by the standard
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414:Unsolved problems in geometry
295:10.1215/S0012-7094-97-08807-4
430:
283:Duke Mathematical Journal
155:Serre's vanishing theorem
335:Smith, Karen E. (2000),
161:, which is optimal for
45:holomorphic line bundle
356:10.1007/s002080000094
344:Mathematische Annalen
256:10.2969/aspm/01010167
82:canonical line bundle
136:Note that for large
213:J. Amer. Math. Soc.
93:spanned by sections
22:Fujita's conjecture
399:Algebraic geometry
209:Lazarsfeld, Robert
58:, the line bundle
26:algebraic geometry
404:Complex manifolds
265:978-4-86497-068-6
195:extension theorem
191:Ohsawa–Takegoshi
163:projective spaces
127:complex dimension
54:complex manifold
30:complex manifolds
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175:Reider's theorem
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409:Conjectures
169:Known cases
18:mathematics
393:Categories
328:0941.32021
201:References
107:very ample
103:+ 1 ;
36:Statement
382:55051810
185:See also
42:positive
374:1764238
320:1453639
303:1455517
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235:1207013
125:is the
71:(where
52:compact
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121:where
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378:S2CID
340:(PDF)
109:when
80:is a
50:on a
260:ISBN
117:+ 2,
28:and
360:hdl
352:doi
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324:Zbl
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221:doi
129:of
84:of
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395::
376:,
370:MR
368:,
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316:MR
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113:≥
99:≥
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48:L
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