Holomorphic Curves into Algebraic Varieties Intersecting Moving Hypersurface Targets
In Ru (Ann. Math. 169 , 255–267 2009 ), Min Ru proved a second main theorem for algebraically nondegenerate holomorphic curves in complex projective varieties intersecting fixed hypersurface targets. In this paper, by introducing a new proof method for the case of projective varieties, we generalize...
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Published in | Acta mathematica vietnamica Vol. 45; no. 1; pp. 291 - 308 |
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Main Authors | , |
Format | Journal Article |
Language | English |
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Springer Singapore
01.03.2020
Springer Nature B.V |
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Abstract | In Ru (Ann. Math.
169
, 255–267
2009
), Min Ru proved a second main theorem for algebraically nondegenerate holomorphic curves in complex projective varieties intersecting fixed hypersurface targets. In this paper, by introducing a new proof method for the case of projective varieties, we generalize this result to moving hypersurface targets. |
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AbstractList | In Ru (Ann. Math. 169, 255–267 2009), Min Ru proved a second main theorem for algebraically nondegenerate holomorphic curves in complex projective varieties intersecting fixed hypersurface targets. In this paper, by introducing a new proof method for the case of projective varieties, we generalize this result to moving hypersurface targets. In Ru (Ann. Math. 169 , 255–267 2009 ), Min Ru proved a second main theorem for algebraically nondegenerate holomorphic curves in complex projective varieties intersecting fixed hypersurface targets. In this paper, by introducing a new proof method for the case of projective varieties, we generalize this result to moving hypersurface targets. |
Author | Van Tan, Tran Dethloff, Gerd |
Author_xml | – sequence: 1 givenname: Gerd surname: Dethloff fullname: Dethloff, Gerd organization: Laboratoire de Mathématiques de Bretagne Atlantique - UMR 6205, Université de Bretagne Occidentale (Brest) – sequence: 2 givenname: Tran surname: Van Tan fullname: Van Tan, Tran email: tantv@hnue.edu.vn organization: Department of Mathematics, Hanoi National University of Education |
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Cites_doi | 10.1007/s11425-010-0039-1 10.1512/iumj.1979.28.28044 10.1007/s11425-012-4378-y 10.1093/imrn/rnu126 10.1155/S107379280210804X 10.1353/ajm.2004.0006 10.1090/S0002-9947-97-01913-2 10.1016/j.jnt.2017.10.008 10.1142/S1793042115500086 10.1353/ajm.2004.0034 10.4007/annals.2009.169.255 10.1007/978-3-211-74280-8_9 10.1007/s00208-018-1661-4 10.1007/s00209-018-2138-6 10.1007/978-3-642-15945-9_3 |
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References | Ru (CR12) 1997; 349 Dethloff, Tan (CR5) 2011; 37 Zariski (CR19) 1937; 41 Hartshorne (CR8) 1977 CR18 Son, Tan, Thin (CR16) 2018; 186 CR17 CR9 Ru (CR13) 2004; 126 Shiffman (CR15) 1979; 28 Chen, Ru, Yan (CR2) 2012; 55 Evertse, Ferretti (CR7) 2008; 16 Le (CR10) 2015; 11 Chen, Ru, Yan (CR3) 2015; 2015 Matsumura (CR11) 1980 Chen, Ru, Yan (CR1) 2010; 53 Corvaja, Zannier (CR4) 2004; 126 Ru (CR14) 2009; 169 Evertse, Ferretti (CR6) 2002; 25 R Hartshorne (336_CR8) 1977 B Shiffman (336_CR15) 1979; 28 O Zariski (336_CR19) 1937; 41 Z Chen (336_CR2) 2012; 55 M Ru (336_CR14) 2009; 169 336_CR18 336_CR17 G Dethloff (336_CR5) 2011; 37 Z Chen (336_CR1) 2010; 53 336_CR9 NT Son (336_CR16) 2018; 186 G Le (336_CR10) 2015; 11 M Ru (336_CR12) 1997; 349 P Corvaja (336_CR4) 2004; 126 H Matsumura (336_CR11) 1980 Z Chen (336_CR3) 2015; 2015 JH Evertse (336_CR7) 2008; 16 JH Evertse (336_CR6) 2002; 25 M Ru (336_CR13) 2004; 126 |
References_xml | – year: 1977 ident: CR8 publication-title: Algebraic Geometry. Grad Texts in Math, vol. 52 contributor: fullname: Hartshorne – volume: 53 start-page: 605 year: 2010 end-page: 616 ident: CR1 article-title: The truncated second main theorem and uniqueness theorems publication-title: Sci. China doi: 10.1007/s11425-010-0039-1 contributor: fullname: Yan – volume: 28 start-page: 627 year: 1979 end-page: 641 ident: CR15 article-title: On holomorphic curves and meromorphic maps in projective space publication-title: Indiana Univ. Math. J. doi: 10.1512/iumj.1979.28.28044 contributor: fullname: Shiffman – ident: CR18 – volume: 55 start-page: 1367 year: 2012 end-page: 1380 ident: CR2 article-title: The degenerated second main theorem and Schmidt’s subspace theorem publication-title: Sci. China doi: 10.1007/s11425-012-4378-y contributor: fullname: Yan – volume: 2015 start-page: 6305 year: 2015 end-page: 6329 ident: CR3 article-title: Schmidt’s subspace theorem with moving hypersurfaces publication-title: Int. Math. Res. Notices doi: 10.1093/imrn/rnu126 contributor: fullname: Yan – volume: 25 start-page: 1295 year: 2002 end-page: 1330 ident: CR6 article-title: Diophantine inequalities on projective varieties publication-title: Internat. Math. Res. Notices doi: 10.1155/S107379280210804X contributor: fullname: Ferretti – volume: 41 start-page: 249 year: 1937 end-page: 265 ident: CR19 article-title: Generalized weight properties of the resultant of n + 1 polynomials in n indeterminates publication-title: Trans. AMS contributor: fullname: Zariski – year: 1980 ident: CR11 publication-title: Commutative Algebra contributor: fullname: Matsumura – volume: 126 start-page: 215 year: 2004 end-page: 226 ident: CR13 article-title: A defect relation for holomorphic curves intersecting hypersurfaces publication-title: Am. J. Math. doi: 10.1353/ajm.2004.0006 contributor: fullname: Ru – volume: 37 start-page: 79 year: 2011 end-page: 111 ident: CR5 article-title: A second main theorem for moving hypersurface targets publication-title: Houston J. Math. contributor: fullname: Tan – ident: CR17 – volume: 349 start-page: 5093 year: 1997 end-page: 5105 ident: CR12 article-title: On a general form of the second main theorem publication-title: Trans. AMS doi: 10.1090/S0002-9947-97-01913-2 contributor: fullname: Ru – volume: 186 start-page: 346 year: 2018 end-page: 369 ident: CR16 article-title: Schmidt’s subspace theorem for moving hypersurface targets publication-title: J. Number Theory doi: 10.1016/j.jnt.2017.10.008 contributor: fullname: Thin – ident: CR9 – volume: 11 start-page: 139 year: 2015 end-page: 158 ident: CR10 article-title: Schmidt’s subspace theorem with moving hypersurfaces publication-title: Int. J. Number Theory doi: 10.1142/S1793042115500086 contributor: fullname: Le – volume: 126 start-page: 1033 year: 2004 end-page: 1055 ident: CR4 article-title: On a general Thue’s equation publication-title: Am. J. Math. doi: 10.1353/ajm.2004.0034 contributor: fullname: Zannier – volume: 169 start-page: 255 year: 2009 end-page: 267 ident: CR14 article-title: Holomorphic curves into algebraic varieties publication-title: Ann. Math. doi: 10.4007/annals.2009.169.255 contributor: fullname: Ru – volume: 16 start-page: 175 year: 2008 end-page: 198 ident: CR7 article-title: A generalization of the subspace theorem with polynomials of higher degree publication-title: Develop. Math. doi: 10.1007/978-3-211-74280-8_9 contributor: fullname: Ferretti – volume: 126 start-page: 1033 year: 2004 ident: 336_CR4 publication-title: Am. J. Math. doi: 10.1353/ajm.2004.0034 contributor: fullname: P Corvaja – volume: 169 start-page: 255 year: 2009 ident: 336_CR14 publication-title: Ann. Math. doi: 10.4007/annals.2009.169.255 contributor: fullname: M Ru – ident: 336_CR9 doi: 10.1007/s00208-018-1661-4 – volume: 2015 start-page: 6305 year: 2015 ident: 336_CR3 publication-title: Int. Math. Res. Notices doi: 10.1093/imrn/rnu126 contributor: fullname: Z Chen – volume: 11 start-page: 139 year: 2015 ident: 336_CR10 publication-title: Int. J. Number Theory doi: 10.1142/S1793042115500086 contributor: fullname: G Le – volume: 55 start-page: 1367 year: 2012 ident: 336_CR2 publication-title: Sci. China doi: 10.1007/s11425-012-4378-y contributor: fullname: Z Chen – volume: 28 start-page: 627 year: 1979 ident: 336_CR15 publication-title: Indiana Univ. Math. J. doi: 10.1512/iumj.1979.28.28044 contributor: fullname: B Shiffman – ident: 336_CR18 doi: 10.1007/s00209-018-2138-6 – volume: 25 start-page: 1295 year: 2002 ident: 336_CR6 publication-title: Internat. Math. Res. Notices doi: 10.1155/S107379280210804X contributor: fullname: JH Evertse – volume: 349 start-page: 5093 year: 1997 ident: 336_CR12 publication-title: Trans. AMS doi: 10.1090/S0002-9947-97-01913-2 contributor: fullname: M Ru – volume-title: Commutative Algebra year: 1980 ident: 336_CR11 contributor: fullname: H Matsumura – ident: 336_CR17 doi: 10.1007/978-3-642-15945-9_3 – volume: 53 start-page: 605 year: 2010 ident: 336_CR1 publication-title: Sci. China doi: 10.1007/s11425-010-0039-1 contributor: fullname: Z Chen – volume-title: Algebraic Geometry. Grad Texts in Math, vol. 52 year: 1977 ident: 336_CR8 contributor: fullname: R Hartshorne – volume: 186 start-page: 346 year: 2018 ident: 336_CR16 publication-title: J. Number Theory doi: 10.1016/j.jnt.2017.10.008 contributor: fullname: NT Son – volume: 16 start-page: 175 year: 2008 ident: 336_CR7 publication-title: Develop. Math. doi: 10.1007/978-3-211-74280-8_9 contributor: fullname: JH Evertse – volume: 126 start-page: 215 year: 2004 ident: 336_CR13 publication-title: Am. J. Math. doi: 10.1353/ajm.2004.0006 contributor: fullname: M Ru – volume: 37 start-page: 79 year: 2011 ident: 336_CR5 publication-title: Houston J. Math. contributor: fullname: G Dethloff – volume: 41 start-page: 249 year: 1937 ident: 336_CR19 publication-title: Trans. AMS contributor: fullname: O Zariski |
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Snippet | In Ru (Ann. Math.
169
, 255–267
2009
), Min Ru proved a second main theorem for algebraically nondegenerate holomorphic curves in complex projective varieties... In Ru (Ann. Math. 169, 255–267 2009), Min Ru proved a second main theorem for algebraically nondegenerate holomorphic curves in complex projective varieties... |
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Title | Holomorphic Curves into Algebraic Varieties Intersecting Moving Hypersurface Targets |
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