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,, \emph{J. Reine Angew. Math.}, 476 (1996), 209. doi: 10.1515/crll.1996.476.209.

[2]

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

[3]

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

[4]

F. Fang, Topology of complete intersections,, \emph{Comment. Math. Helv.}, 72 (1997), 466. doi: 10.1007/s000140050028.

[5]

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

[6]

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

[7]

M. Kreck, Surgery and duality,, \emph{Ann. of Math. (2)}, 149 (1999), 707. doi: 10.2307/121071.

[8]

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

[9]

A. S. Libgober and J. W. Wood, Remarks on moduli spaces of complete intersections,, in \emph{The Lefschetz centennial conference, (1984), 183. 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,, \emph{J. Differential Geom.}, 32 (1990), 139.

[11]

C. Traving, Klassification vollständiger Durchschnitte,, Diplomarbeit, (1985).

show all references

References:
[1]

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

[2]

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

[3]

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

[4]

F. Fang, Topology of complete intersections,, \emph{Comment. Math. Helv.}, 72 (1997), 466. doi: 10.1007/s000140050028.

[5]

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

[6]

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

[7]

M. Kreck, Surgery and duality,, \emph{Ann. of Math. (2)}, 149 (1999), 707. doi: 10.2307/121071.

[8]

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

[9]

A. S. Libgober and J. W. Wood, Remarks on moduli spaces of complete intersections,, in \emph{The Lefschetz centennial conference, (1984), 183. 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,, \emph{J. Differential Geom.}, 32 (1990), 139.

[11]

C. Traving, Klassification vollständiger Durchschnitte,, Diplomarbeit, (1985).

[1]

Alex Eskin, Maryam Mirzakhani. Counting closed geodesics in moduli space. Journal of Modern Dynamics, 2011, 5 (1) : 71-105. doi: 10.3934/jmd.2011.5.71

[2]

Corentin Boissy. Classification of Rauzy classes in the moduli space of Abelian and quadratic differentials. Discrete & Continuous Dynamical Systems - A, 2012, 32 (10) : 3433-3457. doi: 10.3934/dcds.2012.32.3433

[3]

Alex Castro, Wyatt Howard, Corey Shanbrom. Complete spelling rules for the Monster tower over three-space. Journal of Geometric Mechanics, 2017, 9 (3) : 317-333. doi: 10.3934/jgm.2017013

[4]

Christopher Kumar Anand. Unitons and their moduli. Electronic Research Announcements, 1996, 2: 7-16.

[5]

V. Balaji, P. Barik, D. S. Nagaraj. On degenerations of moduli of Hitchin pairs. Electronic Research Announcements, 2013, 20: 103-108. doi: 10.3934/era.2013.20.105

[6]

Hicham Zmarrou, Ale Jan Homburg. Dynamics and bifurcations of random circle diffeomorphism. Discrete & Continuous Dynamical Systems - B, 2008, 10 (2&3, September) : 719-731. doi: 10.3934/dcdsb.2008.10.719

[7]

Zhihong Xia. Homoclinic points and intersections of Lagrangian submanifold. Discrete & Continuous Dynamical Systems - A, 2000, 6 (1) : 243-253. doi: 10.3934/dcds.2000.6.243

[8]

Christian Bonatti, Sylvain Crovisier and Amie Wilkinson. The centralizer of a $C^1$-generic diffeomorphism is trivial. Electronic Research Announcements, 2008, 15: 33-43. doi: 10.3934/era.2008.15.33

[9]

Cheng Cheng, Shaobo Gan, Yi Shi. A robustly transitive diffeomorphism of Kan's type. Discrete & Continuous Dynamical Systems - A, 2018, 38 (2) : 867-888. doi: 10.3934/dcds.2018037

[10]

Michihiro Hirayama, Naoya Sumi. Hyperbolic measures with transverse intersections of stable and unstable manifolds. Discrete & Continuous Dynamical Systems - A, 2013, 33 (4) : 1451-1476. doi: 10.3934/dcds.2013.33.1451

[11]

Françoise Pène. Self-intersections of trajectories of the Lorentz process. Discrete & Continuous Dynamical Systems - A, 2014, 34 (11) : 4781-4806. doi: 10.3934/dcds.2014.34.4781

[12]

Michael Herty, J.-P. Lebacque, S. Moutari. A novel model for intersections of vehicular traffic flow. Networks & Heterogeneous Media, 2009, 4 (4) : 813-826. doi: 10.3934/nhm.2009.4.813

[13]

Michael Herty, S. Moutari, M. Rascle. Optimization criteria for modelling intersections of vehicular traffic flow. Networks & Heterogeneous Media, 2006, 1 (2) : 275-294. doi: 10.3934/nhm.2006.1.275

[14]

Wenxiong Chen, Congming Li. Harmonic maps on complete manifolds. Discrete & Continuous Dynamical Systems - A, 1999, 5 (4) : 799-804. doi: 10.3934/dcds.1999.5.799

[15]

Paula Kemp. Fixed points and complete lattices. Conference Publications, 2007, 2007 (Special) : 568-572. doi: 10.3934/proc.2007.2007.568

[16]

Joachim Escher, Boris Kolev. Right-invariant Sobolev metrics of fractional order on the diffeomorphism group of the circle. Journal of Geometric Mechanics, 2014, 6 (3) : 335-372. doi: 10.3934/jgm.2014.6.335

[17]

Alexandre A. P. Rodrigues. Moduli for heteroclinic connections involving saddle-foci and periodic solutions. Discrete & Continuous Dynamical Systems - A, 2015, 35 (7) : 3155-3182. doi: 10.3934/dcds.2015.35.3155

[18]

Jonathan Chaika, Yitwah Cheung, Howard Masur. Winning games for bounded geodesics in moduli spaces of quadratic differentials. Journal of Modern Dynamics, 2013, 7 (3) : 395-427. doi: 10.3934/jmd.2013.7.395

[19]

Lisa C. Jeffrey and Frances C. Kirwan. Intersection pairings in moduli spaces of holomorphic bundles on a Riemann surface. Electronic Research Announcements, 1995, 1: 57-71.

[20]

Bernd Ammann, Robert Lauter and Victor Nistor. Algebras of pseudodifferential operators on complete manifolds. Electronic Research Announcements, 2003, 9: 80-87.

2016 Impact Factor: 0.483

Metrics

  • PDF downloads (2)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]