2014, 21: 28-40. doi: 10.3934/era.2014.21.28

Remarks on 5-dimensional complete intersections

1. 

Department of Mathematics, School of Science, Tianjin University. Weijin Road 92, Nankai District, Tianjin 300072, China

Received  December 2013 Revised  January 2014 Published  March 2014

This paper will give some examples of diffeomorphic complex 5-dimensional complete intersections and remarks on these examples. Then a result on the existence of diffeomorphic complete intersections that belong to components of the moduli space of different dimensions will be given as a supplement to the results of P.Brückmann (J. reine angew. Math. 476 (1996), 209--215; 525 (2000), 213--217).
Citation: Jianbo Wang. Remarks on 5-dimensional complete intersections. Electronic Research Announcements, 2014, 21: 28-40. doi: 10.3934/era.2014.21.28
References:
[1]

P. Brückmann, A remark on moduli spaces of complete intersections, J. Reine Angew. Math., 476 (1996), 209-215. doi: 10.1515/crll.1996.476.209.

[2]

P. Brückmann, A remark on moduli spaces of 4-dimensional complete intersections, J. Reine Angew. Math., 525 (2000), 213-217. doi: 10.1515/crll.2000.068.

[3]

W. Ebeling, An example of two homeomorphic, nondiffeomorphic complete intersection surfaces, Invent. Math., 99 (1990), 651-654. doi: 10.1007/BF01234435.

[4]

F. Fang, Topology of complete intersections, Comment. Math. Helv., 72 (1997), 466-480. doi: 10.1007/s000140050028.

[5]

F. Fang and S. Klaus, Topological classification of 4-dimensional complete intersections, Manuscript Math., 90 (1996), 139-147. doi: 10.1007/BF02568299.

[6]

F. Fang and J. Wang, Homeomorphism classification of complex projective complete intersections of dimensions 5, 6 and 7, Math. Z., 266 (2010), 719-746. doi: 10.1007/s00209-009-0597-5.

[7]

M. Kreck, Surgery and duality, Ann. of Math. (2), 149 (1999), 707-754. doi: 10.2307/121071.

[8]

A. S. Libgober and J. W. Wood, Differentiable structures on complete intersections. I, Topology, 21 (1982), 469-482. doi: 10.1016/0040-9383(82)90024-6.

[9]

A. S. Libgober and J. W. Wood, Remarks on moduli spaces of complete intersections, in The Lefschetz centennial conference, Part I (Mexico City, 1984), Contemp. Math., 58, Amer. Math. Soc., Providence, RI, 1986, 183-194. doi: 10.1090/conm/058.1/860413.

[10]

A. S. Libgober and J. W. Wood, Uniqueness of the complex structure on Kähler manifolds of certain homotopy types, J. Differential Geom., 32 (1990), 139-154.

[11]

C. Traving, Klassification vollständiger Durchschnitte, Diplomarbeit, University of Mainz, 1985. Available from: http://www.mfo.de/Staff/traving.pdf

show all references

References:
[1]

P. Brückmann, A remark on moduli spaces of complete intersections, J. Reine Angew. Math., 476 (1996), 209-215. doi: 10.1515/crll.1996.476.209.

[2]

P. Brückmann, A remark on moduli spaces of 4-dimensional complete intersections, J. Reine Angew. Math., 525 (2000), 213-217. doi: 10.1515/crll.2000.068.

[3]

W. Ebeling, An example of two homeomorphic, nondiffeomorphic complete intersection surfaces, Invent. Math., 99 (1990), 651-654. doi: 10.1007/BF01234435.

[4]

F. Fang, Topology of complete intersections, Comment. Math. Helv., 72 (1997), 466-480. doi: 10.1007/s000140050028.

[5]

F. Fang and S. Klaus, Topological classification of 4-dimensional complete intersections, Manuscript Math., 90 (1996), 139-147. doi: 10.1007/BF02568299.

[6]

F. Fang and J. Wang, Homeomorphism classification of complex projective complete intersections of dimensions 5, 6 and 7, Math. Z., 266 (2010), 719-746. doi: 10.1007/s00209-009-0597-5.

[7]

M. Kreck, Surgery and duality, Ann. of Math. (2), 149 (1999), 707-754. doi: 10.2307/121071.

[8]

A. S. Libgober and J. W. Wood, Differentiable structures on complete intersections. I, Topology, 21 (1982), 469-482. doi: 10.1016/0040-9383(82)90024-6.

[9]

A. S. Libgober and J. W. Wood, Remarks on moduli spaces of complete intersections, in The Lefschetz centennial conference, Part I (Mexico City, 1984), Contemp. Math., 58, Amer. Math. Soc., Providence, RI, 1986, 183-194. doi: 10.1090/conm/058.1/860413.

[10]

A. S. Libgober and J. W. Wood, Uniqueness of the complex structure on Kähler manifolds of certain homotopy types, J. Differential Geom., 32 (1990), 139-154.

[11]

C. Traving, Klassification vollständiger Durchschnitte, Diplomarbeit, University of Mainz, 1985. Available from: http://www.mfo.de/Staff/traving.pdf

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