A few remarks on sections of the Picard bundle of family of curves
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918341130584064 |
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| author | Fassina, Lorenzo Pirola, Gian Pietro |
| author_facet | Fassina, Lorenzo Pirola, Gian Pietro |
| contents | We study sections of the relative Picard bundle of a family of curves of genus $g \geq 2$ through the rank of the associated normal function. Using Griffiths' formula for the infinitesimal invariant and higher Schiffer variations, we establish a numerical inequality relating the rank, the minimal support of a representing divisor and the modular dimension of the family. When the modular map is dominant, we obtain a sharp classification: equality occurs only for multiples of odd theta characteristics or of the canonical section. As applications, we derive geometric consequences for plane curves, obtaining results on intersections with very general quartic curves, in the spirit of the work of Chen-Riedl-Yeong, and with quintic curves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_14888 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A few remarks on sections of the Picard bundle of family of curves Fassina, Lorenzo Pirola, Gian Pietro Algebraic Geometry We study sections of the relative Picard bundle of a family of curves of genus $g \geq 2$ through the rank of the associated normal function. Using Griffiths' formula for the infinitesimal invariant and higher Schiffer variations, we establish a numerical inequality relating the rank, the minimal support of a representing divisor and the modular dimension of the family. When the modular map is dominant, we obtain a sharp classification: equality occurs only for multiples of odd theta characteristics or of the canonical section. As applications, we derive geometric consequences for plane curves, obtaining results on intersections with very general quartic curves, in the spirit of the work of Chen-Riedl-Yeong, and with quintic curves. |
| title | A few remarks on sections of the Picard bundle of family of curves |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2602.14888 |