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Moduli spaces of 6 and 7-dimensional complete intersections. (English) Zbl 1342.14101

In their paper [Contemp. Math. 58, 183–194 (1986; Zbl 0605.14010)], A. S. Libgober and J. W. Wood showed the existence of homeomorphic complete intersections of dimension 2 and diffeomorphic ones of dimension 3 that belong to components of the moduli space having different dimensions. Then in [J. Reine Angew. Math. 476, 209–215 (1996; Zbl 0847.14003); ibid. 525, 231–217 (2000; Zbl 0992.14015)] P. Brückmann constructed examples of homeomorphic complete intersections of dimension 2 and 4 that belong to components of the moduli space of different dimensions. The authors of the present paper, using their results in [F. Fang and J. Wang, Math. Z. 266, No. 3, 719–746 (2010; Zbl 1207.57032); Electron. Res. Announc. Math. Sci. 21, 28–40 (2014; Zbl 1303.14055)] show that there exist homeomorphic (diffeomorphic) complex 6-dimensional (7-dimensional) complete intersections which lie in different dimensional components of the moduli space.

MSC:

14M10 Complete intersections
14J15 Moduli, classification: analytic theory; relations with modular forms
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References:

[1] Brückmann, P., A remark on moduli spaces of complete intersections, J. Reine Angew. Math., 476, 209-215 (1996) · Zbl 0847.14003
[2] Brückmann, P., A remark on moduli spaces of 4-dimensional complete intersections, J. Reine Angew. Math., 525, 213-217 (2000) · Zbl 0992.14015
[3] Chen, S., Equal products and equal sums of like powers
[4] Choudhry, A., Equal sums of like powers and equal products of integers, Rocky Mountain J. Math., 43, 763-792 (2013) · Zbl 1355.11022
[5] Fang, F.; Wang, J., Homeomorphism classification of complex projective complete intersections of dimensions 5, 6 and 7, Math. Z., 266, 719-746 (2010) · Zbl 1207.57032
[6] Kreck, M., Surgery and duality, Ann. of Math., 149, 3, 707-754 (1999) · Zbl 0935.57039
[7] Libgober, A.; Wood, J., Differentiable structures on complete intersections, I., Topology, 21, 469-482 (1982) · Zbl 0504.57015
[8] Libgober, A.; Wood, J., Remarks on moduli spaces of complete intersections, Contemp. Math., 58, 183-194 (1986) · Zbl 0605.14010
[9] Narasimhan, M.; Simha, R., Manifolds with ample canonical class, Invent. Math., 5, 120-128 (1968) · Zbl 0159.37902
[10] Traving, C., Klassification vollständiger Durchschnitte (1985), University of Mainz, available from:
[11] Wang, J., Remarks on 5-dimensional complete intersections, Electron. Res. Announc. Math. Sci., 21, 28-40 (2014) · Zbl 1303.14055
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