On the strong base locus of a projective variety
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866912968254423040 |
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| author | Ballico, Edoardo Brambilla, Maria Chiara Santarsiero, Pierpaola |
| author_facet | Ballico, Edoardo Brambilla, Maria Chiara Santarsiero, Pierpaola |
| contents | We introduce and study the base locus and the strong base locus of a projective variety X. The base locus of X parametrizes configurations of smooth points of X where the span of the tangent spaces of X at these points intersects X at some additional smooth point. The strong base locus parametrizes configurations of smooth points of X for which the span of the tangent spaces of X at the given configuration contains the entire tangent space at an additional point.
These notions originate from the study of base loci of tangential projections, are strictly related to interpolation problems with double points in special position, and provide a natural framework to study tangential contact for nongeneral points. We give first properties and explore connections with Terracini loci and with the concept of identifiability. We focus on tensor-related varieties and characterize the nonemptiness of base loci and strong base loci for Veronese and Segre-Veronese varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_15103 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the strong base locus of a projective variety Ballico, Edoardo Brambilla, Maria Chiara Santarsiero, Pierpaola Algebraic Geometry Primary 14N07, Secondary 14N05, 14M99 We introduce and study the base locus and the strong base locus of a projective variety X. The base locus of X parametrizes configurations of smooth points of X where the span of the tangent spaces of X at these points intersects X at some additional smooth point. The strong base locus parametrizes configurations of smooth points of X for which the span of the tangent spaces of X at the given configuration contains the entire tangent space at an additional point. These notions originate from the study of base loci of tangential projections, are strictly related to interpolation problems with double points in special position, and provide a natural framework to study tangential contact for nongeneral points. We give first properties and explore connections with Terracini loci and with the concept of identifiability. We focus on tensor-related varieties and characterize the nonemptiness of base loci and strong base loci for Veronese and Segre-Veronese varieties. |
| title | On the strong base locus of a projective variety |
| topic | Algebraic Geometry Primary 14N07, Secondary 14N05, 14M99 |
| url | https://arxiv.org/abs/2603.15103 |