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In this paper we study arithmetically Cohen-Macaulay (ACM for short) vector bundles ε of rank ≥ 3 on hypersurfaces
X_r ⊂P^4 of degree r≥1.
We consider here
mainly the case of degree r = 4, which is the first
unknown case in literature.
Under some natural conditions for
the bundle ε we derive a list of possible Chern classes (c_1,c_2,c_3)
which may arise in the cases of rank k=3 and k=4, when r=4 and we give
several examples.
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참고문헌 (23)
참고문헌 신청
A. Iliev / 2000 / Quartic 3-fold: Pfaffians, vector bundles, and halfcanonical curves / Michigan Math. J. 47 (2) : 385 ~ 394
A. Vogeelar / 1978 / Constructing vector bundles from codimension-two subvarieties / 박사
B. G. Mo˘ıˇsezon / 1967 / Algebraic homology classes on algebraic varieties / Izv. Akad. Nauk SSSR Ser. Mat. 31 : 225 ~ 268
C. Madonna / 1998 / A splitting criterion for rank 2 vector bundles on hypersurfaces in P4 / Rend. Sem. Mat. Univ. Politec. Torino 56 (2) : 43 ~ 54
C. Madonna / 2000 / Rank-two vector bundles on general quartic hypersurfaces in P4 / Rev. Mat. Complut. 13 (2) : 287 ~ 301
A. Vogeelar / 1978 / Constructing vector bundles from codimension-two subvarieties / 박사
B. G. Mo˘ıˇsezon / 1967 / Algebraic homology classes on algebraic varieties / Izv. Akad. Nauk SSSR Ser. Mat. 31 : 225 ~ 268
C. Madonna / 1998 / A splitting criterion for rank 2 vector bundles on hypersurfaces in P4 / Rend. Sem. Mat. Univ. Politec. Torino 56 (2) : 43 ~ 54
C. Madonna / 2000 / Rank-two vector bundles on general quartic hypersurfaces in P4 / Rev. Mat. Complut. 13 (2) : 287 ~ 301
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