Arrondo Esteban, Enrique and Maddona, Carlo G. (2009) Curves and vector bundles on quartic threefolds. Journal of the Korean Mathematical Society, 46 (3). pp. 589-608. ISSN 0304-9914
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Official URL: http://arxiv.org/pdf/math/0703413v4.pdf
In this paper we study arithmetically Cohen-Macaulay (ACM for short) vector bundles E of rank k 3 on hypersurfaces Xr P4 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 E we derive a list of possible Chern classes (c1, c2, c3) which may arise in the cases of rank k = 3 and k = 4, when r = 4 and we give several examples.
|Uncontrolled Keywords:||Intermediate cohomology; Criterion; Quartic threefold; ACM bundle; Projectively normal curve|
|Subjects:||Sciences > Mathematics > Algebraic geometry|
 E. Arbarello, M. Cornalba, P.A. Griffiths and J. Harris, Geometry of
Algebraic Curves, Springer, 1985.
 E. Arbarello and E. Sernesi, Petri’s approach to the study of the ideal
associated to a special divisor, Inventiones Math. 49(1978), 99–119.
 E. Arrondo, A home-made Hartshorne-Serre correspondence, Rev.Mat.
Complut. 20 (2007), no. 2, 423–443.
 E. Arrondo and L. Costa, Vector bundles on Fano 3–folds without intermediate
cohomology, Comm. Algebra 28 (2000), no. 8, 3899–3911.
 E. Arrondo and D. Faenzi, Vector bundles with no intermediate cohomology
on Fano threefolds of type V22, Pacific J. Math. 225 (2006), no.
 J. Carlson, M. Green, P. Griffiths and J. Harris, Infinitesimal variations
of Hodge structures (I), Comp. Math. 50 (1983), 105–205.
 L. Chiantini and C. Madonna, ACM bundles on a general quintic threefold,
Matematiche (Catania) 55(2000), no.2, 239–258.
 L. Chiantini and C. Madonna, A splitting criterion for rank 2 vector
bundles on a general sextic threefold, Internat. J. Math. 15(2004), no.4,
 L. Chiantini and C.Madonna, ACM bundles on general hypersurfaces
in P5 of low degree, Collect. Math. Vol. 56(2005), no. 1, 85-96.
 D. Eisenbud, Commutative algebra with a view toward algebraic geometry,
 D. Eisenbud, J. Koh, and M. Stillman, Determinantal Equations for
Curves of High Degree Amer. J. Math. Vol. 110(1988), no. 3, pp. 513-
 D. Faenzi, Bundles over the Fano threefold V5, Comm. Algebra
33(2005), no. 9, 3061–3080.
 W. Fulton, Intersection theory, Springer 1998.
 J. Harris, M. Roth and J. Starr, Curves of small degree on cubic threefolds,
Rocky Mountain J. Math. 35(2005), no. 3, 761–817.
 G. Horrocks, Vector bundles on the punctured spectrum of a local ring,
Proc. London Math. Soc. 14 (1964), 689-713.
 A. Iliev and D. Markushevich, Quartic 3-folds: pfaffians, vector bundles,
and half-canonical curves, Mich. Math. J. 47 (2000), 385–394.
 A. Iliev and L. Manivel, Pfaffian lines and vector bundles on Fano
threefolds of genus 8, J. Alg. Geom., to appear.
 N.M. Kumar, A.P. Rao and G.V. Ravindra, Arithmetically Cohen-
Macaulay bundles on three dimensional hypersurfaces, Int. Math. Res.
Not. IMRN 2007, no. 8, Art. ID rnm025, 11 pp.
 C. Madonna, A splitting criterion for rank 2 vector bundles on hypersurfaces
in P4, Rend. Sem. Mat. Univ. Pol. Torino 56 (1998), no.2,
 C. Madonna, Rank–two vector bundles on general quartic hypersurfaces
in P4, Rev. Mat. Complut. XIII (2000), num.2, 287–301.
 C.G.Madonna, ACM vector bundles on prime Fano threefolds and complete
intersection Calabi Yau threefolds, Rev. Roumaine Math. Pures
Appl. 47(2002) no.2, 211-222.
 C. Madonna, Rank 4 vector bundles on the quintic threefold, CEJM 3
(2005), no.3, 404–411.
 S. Mori, On degrees and genera of curves on smooth quartic surfaces
in P3, Nagoya Math. J. 96(1984), 127–132.
 B.G. Mo˘ıˇsezon, Algebraic homology classes on algebraic varieties, Izv.
Akad. Nauk SSSR Ser. Mat. 31 (1967) 225–268.
|Deposited On:||18 Apr 2012 10:30|
|Last Modified:||18 Apr 2012 10:30|
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