Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Nodal quintic threefolds and nodal octic surfaces


Author: Ciprian Borcea
Journal: Proc. Amer. Math. Soc. 109 (1990), 627-635
MSC: Primary 14J30; Secondary 14J25
MathSciNet review: 1021895
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The relation between the nodes and the defect of nodal quintic threefolds or double solids ramified over nodal octic surfaces has implications on the existence of such varieties with fewer nodes.


References [Enhancements On Off] (What's this?)

  • [1] M. F. Atiyah, On analytic surfaces with double points, Proc. Roy Soc. London Ser. A 245 (1958), 237-244. MR 0095974 (20:2472)
  • [2] J. W. Bruce, On complex projective hypersurfaces, Proc. Edinburgh Math. Soc. 24 (1981), 91-97. MR 625281 (82i:14007)
  • [3] F. Catanese and G. Ceresa, Constructing sextic surfaces with a given number d of nodes, J. Pure Appl. Algebra 23 (1982), 1-12. MR 638117 (83a:14030)
  • [4] H. Clemens, Double solids, Adv. in Math. 47 (1983), 107-230. MR 690465 (85e:14058)
  • [5] H. Flenner and S. Kosarew, On locally trivial deformations, Publ. Res. Inst. Math. Sci. 23 (1987), 627-665. MR 918518 (89c:32055)
  • [6] R. Friedman, Simultaneous resolution of threefold double points, Math. Ann. 274 (1986), 671-689. MR 848512 (87k:32035)
  • [7] D. Gallarati, Una superficie dell'ottavo ordine con 160 nodi, Acc. Ligure Sci. lett. 14 (1957), 1-7.
  • [8] B. van Geemen and J. Werner, Nodal quintics in $ {P^4}$, preprint.
  • [9] G. M. Greuel and U. Karras, Families of varieties with prescribed singularities, Compositio Math. 69 (1989), 83-110. MR 986814 (90d:32037)
  • [10] F. Hirzebruch, Some examples of threefolds with trivial canonical bundle, Collected Papers II (no. 75), Springer-Verlag, Heidelberg, 1987, pp. 757-770.
  • [11] K. Hulek, Projective geometry of elliptic curves, Astérisque, Soc. Math. de France, 1986. MR 845383 (88c:14046)
  • [12] O. Kreiss, Über syzygetische Flächen, Annali di Mat. 41 (1956), 105-111. MR 0078744 (17:1240h)
  • [13] N. Manolache, On the normal bundle to Abelian surfaces embedded in $ {P^4}(C)$, Manuscripta Math. 55 (1986), 111-119. MR 828415 (87d:14011)
  • [14] Y. Miyaoka, The maximal number of quotient singularities on surfaces with given numerical invariants, Math. Ann. 268 (1984), 159-171. MR 744605 (85j:14060)
  • [15] Ch. Schoen, Algebraic cycles on certain desingularized nodal hypersurfaces, Math. Ann. 279 (1985), 17-27. MR 769603 (86d:14010)
  • [16] -, On the geometry of a special determinantal hypersurface associated to the Mumford-Horrocks vector bundle, J. Reine Angew. Math. 364 (1986), 85-111. MR 817640 (87e:14039)
  • [17] -, On fibre products of rational elliptic surfaces with section, Math. Z. 197 (1988), 177-199. MR 923487 (89c:14062)
  • [18] A. Stromingerand E. Witten, New manifolds for supersiring compactification, Comm. Math. Phys. 101 (1985), 341-361. MR 815189 (87c:81153)
  • [19] G. Tian, Smoothness of the universal deformation space of compact Calabi-Yau manifolds and its Peterson-Weil metric, Mathematical Aspects of String Theory (S. T. Yau, ed.), World Scientific, Singapore, 1987. MR 915841
  • [20] A. N. Varchenko, On semicontinuity of the spectrum and an upper bound for the number of singular points of projective hypersurfaces, Dokl. Akad. Nauk USSR 270 (1983). (Russian) MR 712934 (85d:32028)
  • [21] J. Wehler, Cyclic coverings: deformation and Torelli theorem, Math. Ann. 274 (1986), 443-472. MR 842625 (87i:32030)
  • [22] J. Werner, Kleine Auflösungen spezieller dreidimensionaler Varietäten, Bonner Math. Schriften 186 (1987). MR 930270 (89k:14018)
  • [23] -, (with an appendix by B. van Geemen), New examples of threefolds with $ {c_1} = 0$, preprint.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 14J30, 14J25

Retrieve articles in all journals with MSC: 14J30, 14J25


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1021895-0
PII: S 0002-9939(1990)1021895-0
Article copyright: © Copyright 1990 American Mathematical Society