On homogeneous polynomials determined by their Jacobian ideal

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• 作者：Zhenjian Wang (1)
  
  1. CNRS ; LJAD ; UMR 7351 ; University of Nice Sophia Antipolis ; 06100 ; Nice ; France
  
• 关键词：Primary 14A25 ; Secondary 14C34 ; 14J70
• 刊名：manuscripta mathematica
• 出版年：2015
• 出版时间：March 2015
• 年：2015
• 卷：146
• 期：3-4
• 页码：559-574
• 全文大小：182 KB
• 参考文献：1. Carlson, J., Griffiths, P.: Infinitesimal variations of Hodge structure and the global Torelli problem. In: Beauville, A. (Ed.) Journ茅es de G茅ometrie Alg茅brique d鈥橝ngers, pp. 51鈥?6. Sijthoff and Noordhoff (1980)
  2. Dimca, A.: On the Syzygies and Hodge Theory of Nodal Hypersurfaces, arXiv:1310.5344
  3. Dimca, A.: Jacobian Syzygies and Torelli Properties for Projective Hypersurfaceswith Isolated Singularities, arXiv:1408.2244
  4. Dimca, A., Sernesi, E.: Syzygies and Logarithmic Vector Fields Along Plane Curves, arXiv:1401.6838
  5. Dimca A., Sticlaru G.: On the syzygies and Alexander polynomials of nodal hypersurfaces. Math. Nachr. 285, 2120鈥?128 (2012) CrossRef
  6. Dimca, A., Sticlaru, G.: Koszul complexes and pole order filtrations. Proc. Edinb. Math. Soc. (to appear), arXiv:1108.3976
  7. Dimca, A., Saito, M.: Generalization of theorems of Griffiths and Steenbrink to Hypersurfaces with Ordinary Double Points, arXiv:1403.4563v4
  8. Donagi R.: Generic Torelli for projective hypersurfaces. Compos. Math. 50, 325鈥?53 (1983)
  9. Matsumura H., Monsky P.: On the automorphisms of hypersurfaces. J. Math. Kyoto Univ. 3, 347鈥?61 (1964)
  10. Milnor J.: Singular Points of Complex Hypersurfaces. Ann. of Math. Studies, vol. 61. Princeton University Press, Princeton (1968)
  11. Ueda K., Yoshinaga M.: Logarithmic vector fields along smooth divisors in projective spaces. Hokkaido Math. J. 38, 409鈥?15 (2009) CrossRef
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Algebraic Geometry
  Topological Groups and Lie Groups
  Geometry
  Number Theory
  Calculus of Variations and Optimal Control
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-1785

文摘

We investigate which homogeneous polynomials are determined by their Jacobian ideals, and extend and complete previous results due to J. Carlson and Ph. Griffiths, K. Ueda and M. Yoshinaga, and A. Dimca and E. Sernesi.