Abstract
We demonstrate that many families of Calabi-Yau threefolds consist generically of small resolutions of nodal forms in other families and, in fact, that a large class of families is connected by this relation. Our result resonates with a conjecture of Reid that Calabi-Yau threefolds may have a universal moduli space even though they are of different homotopy types. Such ideas tie quite naturally to alluring prospects of unifying (super)string models.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Hübsch T.: Calabi-Yau Manifolds-Motivations and Constructions, Commun. Math. Phys.108, 291 (1987). Manifold compactification of superstrings. in: Superstrings, unified theories and cosmology. Furlan G., Jengo R., Pati J.C., Sciama D.W., Sezgin E., Shafi Q., (eds.) (Singapore: World Scientific, 1987; Green P., Hübsch T.: Calabi-Yau manifolds as complete intersections in products of complex projective spaces. Commun. Math. Phys.109, 99 (1987). Polynomial deformations and cohomology of Calabi-Yau manifolds. Commun. Math. Phys.113, 505 (1987), Calabi-Yau hypersurfaces in products of semi-ample surfaces. Commun. Math. Phys.115, 231(1988). Green P., Lütken C.A., Hübsch T.: All the hodge numbers of all complete intersection Calabi-Yau manifolds. University of Texas report UTTG-29-87; Candelas P., Lütken C.A., Schimmrigk R.: Complete intersection Calabi-Yau manifolds II. University of Texas report UTTG-11-87
Candelas P., Dale A.M., Lütken C.A., Schimmrigk R.: Complete intersection Calabi-Yau manifolds. University of Texas report UTTG-10-87
Clemens C.H.: Double solids, Adv. Math.47, 107 (1983)
Reid M.: The moduli space of 3-folds withK=0 may nevertheless be irreducible Math. Ann.278, 329 (1987)
Atiyah M.F.: On analytic surfaces with double points. Proc. Roy. Soc.A247, 237 (1958)
Hirzebruch F., Werner J.: Some examples of Threefolds with Trivial Canonical Class. Max. Planck Institut für Mathematik (Bonn) Report SFB/MPI 85-58
Grauert H.: Über Modifikationen und exzeptionelle analytische Mengen. Math. Ann.146, 331 (1962); Artin: M. Algebraization of formal moduli. II. Existence of modifications. Ann. Math.91, 88 (1970)
Green P.S., Hübsch: T. Determinantal singularities on Fourfolds and Discriminantal Singularities on Threefolds. (to appear)
Reifeartaigh: L.O.: Group structure of gauge theories. Cambridge: Cambridge Press 1986, esp. Chap. 8 and 12 and references therein. For some sample computations see, e.g.,: Kim J.S.: Nucl. Phys.B196, 285 (1982); Abud, M. Anastaze, G. Eckert P., Ruegg H.: Ann. Phys. (NY)162, 155 (1985); Kaymakcalan, Ö., Michel L., Wali K., McGlinn W.D., Reifeartaigh: L.O.: Nucl. Phys.B267, 203 (1986); Cummings C.J., King R.C.: J. Phys.A19, 161 (1986)
Author information
Authors and Affiliations
Additional information
Communicated by S.-T. Yau
Supported by the Robert A. Welch Foundation and NSF Grants: PHY 8503890 and PHY 8605978
On leave from “Ruder Bošković” Institute, Bijenička 54, YU-41000 Zagreb, Croatia, Yugoslavia
Rights and permissions
About this article
Cite this article
Green, P.S., Hübsch, T. Connecting moduli spaces of Calabi-Yau threefolds. Commun.Math. Phys. 119, 431–441 (1988). https://doi.org/10.1007/BF01218081
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01218081