A Syzygy Rank Characterization of Strongly Euler Homogeneity for Projective Hypersurfaces
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916991006146560 |
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| author | Liao, Xia Zhang, Xiping |
| author_facet | Liao, Xia Zhang, Xiping |
| contents | In this paper we give a characterization of strongly Euler homogeneous singular points on a reduced complex projective hypersurface $D=V(f)\subset \PP^n$ using the Jacobian syzygies of $f$. The characterization compares the ranks of the first syzygy matrices of the global Jacobian ideal $J_f$ and its quotient $J_f/(f)$. When $D$ has only isolated singularities, our characterization refines a recent result of Andrade-Beorchia-Dimca-Miró-Roig. We also prove a generalization of this characterization to smooth projective toric varieties. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_04482 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Syzygy Rank Characterization of Strongly Euler Homogeneity for Projective Hypersurfaces Liao, Xia Zhang, Xiping Algebraic Geometry 14B05, 14C17, 32S60 In this paper we give a characterization of strongly Euler homogeneous singular points on a reduced complex projective hypersurface $D=V(f)\subset \PP^n$ using the Jacobian syzygies of $f$. The characterization compares the ranks of the first syzygy matrices of the global Jacobian ideal $J_f$ and its quotient $J_f/(f)$. When $D$ has only isolated singularities, our characterization refines a recent result of Andrade-Beorchia-Dimca-Miró-Roig. We also prove a generalization of this characterization to smooth projective toric varieties. |
| title | A Syzygy Rank Characterization of Strongly Euler Homogeneity for Projective Hypersurfaces |
| topic | Algebraic Geometry 14B05, 14C17, 32S60 |
| url | https://arxiv.org/abs/2510.04482 |