Hostname: page-component-8448b6f56d-xtgtn Total loading time: 0 Render date: 2024-04-24T17:33:06.214Z Has data issue: false hasContentIssue false
  • English
  • Français

On Deformations of Nodal Hypersurfaces

Published online by Cambridge University Press:  20 November 2018

Zhenjian Wang
Zhenjian Wang*
Affiliation:
Univ. Côte d’Azur, CNRS, LJAD, UMR 7351, 06100 Nice, France, e-mail : wzhj01@gmail.com
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We extend the infinitesimal Torelli theorem for smooth hypersurfaces to nodal hypersurfaces.

Keywords

32S3514C3014D0732S25nodal hypersurfacedeformationTorelli theorem
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 61 , Issue 3 , 01 September 2018 , pp. 659 - 672
Copyright
Copyright © Canadian Mathematical Society 2018

References

[1] Dimca, A., Topics on real and complex singularities. An introduction Advanced Lectures in Mathematics, Friedr Vieweg & Sohn, Braunschweig, 1987. http://dx.doi.org/10.1007/978-3-663-13903-4Google Scholar
[2] Dimca, A., Singularities and topology of hypersurfaces. Universitext, Springer-Verlag, New York, 1992. http://dx.doi.org/10.1007/978-1-4612-4404-2Google Scholar
[3] Dimca, A., Hodge number of hypersurfaces. Abh. Math. Sem. Univ. Hamburg 66 (1996), 377–386. http://dx.doi.org/10.1007/BF02940815Google Scholar
[4] Dimca, A., Syzygies offacobian ideals and defects of linear Systems. Bull. Math. Soc. Sei. Math. Roumanie (N.S.) 56(2013), no. 2, 191–203.Google Scholar
[5] Dimca, A., On the syzygies and Hodge theory ofnodal hypersurfaces. Ann. Univ. Ferrara Sez. VII Sei. Mat. 63 (2017), no. 1, 87–101. http://dx.doi.Org/10.1007/s11565-017-0278-yGoogle Scholar
[6] Dimca, A. and Saito, M., Generaüzation oftheorems ofGriffiths and Steenbrink to hypersurfaces with ordinary doublepoints. arxiv:1403.4563v4Google Scholar
[7] Dimca, A., Saito, M., and Wotzlaw, L., A generalization ofGriffiths’ theorem on rational integrals. II. Michigan Math. J. 58 (2009), 603–625. http://dx.doi.org/10.1307/mmjV1260475692Google Scholar
[8] Durfee, A. H., Mixed Hodge struetures on punetured neighbourhoods. Duke Math. J. 50 (1983), no. 4, 1017–1040. http://dx.doi.org/10.1215/S0012-7094-83-05043-3Google Scholar
[9] Hamm, H. A., Lefschetz theorems for Singular varieties. Part I (Arcata, Calif., 1981) Proc. Sympos. Pure Math., 40, American Mathematical Society, Providence, RI, 1983, pp. 547-557.Google Scholar
[10] Mather, J., Notes on topological stability. Harvard University, 1970.Google Scholar
[11] Peters, C. and Steenbrink, J., Mixed Hodge struetures. Ergebnisse der Mathematik und ihrer Grenzgebiete, 3, Folge, A Series of Modern Surveys in Mathematics, 52, Springer, Berlin, 2008.Google Scholar
[12] Voisin, C., Hodge theory and complex algebraic geometry. I. Cambriddge Studies in Advanced Mathematics, 77, Cambridge University Press, Cambridge, 2003. http://dx.doi.org/10.1017/CBO9780511615177Google Scholar
[13] Voisin, C., Hodge theory and complex algebraic geometry. II. Cambridge Studies in Advanced Mathematics, 77, Cambridge University Press, Cambridge, 2003. http://dx.doi.org/10.1017/CBO9780511615177Google Scholar
[14] Wang, Z., On homogeneous polynomials determined by their Jacobian ideal. Manuscripta Math. 146 (2015), 559–574. http://dx.doi.org/10.1007/s00229-014-0703-9Google Scholar
[15] Zhao, Y., Deformations ofnodal surfaces. PhD thesis, Leiden University, 2016. https://openaccess.leidenuniv.nl/handle/1887/44549Google Scholar