Abstract
In this article, we give a higher dimensional analogue of Severi’s result that the singular points of nodal hypersurfaces of degree m in the projective space \(\mathbb{P}^3\) impose linearly independent conditions on forms of degree d ≥ 2m−5 in \(\mathbb{P}^3\).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Cheltsov I. (2005) On factoriality of nodal threefolds. J. Alg. Geometry 14, 663–690
Ein, L.: Multiplier ideals, vanishing theorems and applications. In: Algebraic geometry – Santa Cruz 1995, Proceedings of Symposium on Pure Mathematics 62, pp. 203–219, American Mathematical Society Providence, RI (1997)
Kollár J., Mori S. (1998) Birational Geometry of Algebraic Varieties, (English edition). Cambridge University Press, Cambridge
Lazarsfeld R. (2004) Positivity in Algebraic Geometry II: Positivity for Vector Bundles, and Multiplier Ideals. Springer Heidelberg New York, Berlin
Nadel A. (1990) Multiplier ideal sheaves and Kähler-Einstein metrics of positive scalar curvature. Ann. Math. 132(2):549–596
Nobile A. (1986) Surfaces with nodes in projective space. J. Pure Appl. Algebra 42, 275–285
Severi F. (1946) Sul massimo numero di nodi di una superficie de dato ordine dello spazio ordinario o di una forma di un iperspazio. Ann. Mat. Pura. Appl. 25, 1–41
Author information
Authors and Affiliations
Corresponding author
Additional information
This work has been partially supported by KOSEF Grant R01-2005-000-10771-0.
Rights and permissions
About this article
Cite this article
Park, J., Woo, Y. A remark on hypersurfaces with isolated singularities. manuscripta math. 121, 451–456 (2006). https://doi.org/10.1007/s00229-006-0047-1
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00229-006-0047-1