American Institute of Mathematical Sciences

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

Remarks on 5-dimensional complete intersections

Jianbo Wang 1,

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).
Keywords: Complete intersections, diffeomorphism, moduli space..
Mathematics Subject Classification: Primary: 14M10, 14J15, 57R50; Secondary: 57R19, 14D2.
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.  Google Scholar

[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.  Google Scholar

[3]

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

[4]

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

[5]

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

[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.  Google Scholar

[7]

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

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[11]

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

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.  Google Scholar

[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.  Google Scholar

[3]

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

[4]

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

[5]

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

[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.  Google Scholar

[7]

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

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[11]

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

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