Maximum number of zeroes of polynomials on weighted projective spaces over a finite field
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909712301162496 |
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| author | Nardi, Jade San-José, Rodrigo |
| author_facet | Nardi, Jade San-José, Rodrigo |
| contents | We compute the maximum number of rational points at which a homogeneous polynomial can vanish on a weighted projective space over a finite field, provided that the first weight is equal to one. This solves a conjecture by Aubry, Castryck, Ghorpade, Lachaud, O'Sullivan and Ram, which stated that a Serre-like bound holds with equality for weighted projective spaces when the first weight is one, and when considering polynomials whose degree is divisible by the least common multiple of the weights. We refine this conjecture by lifting the restriction on the degree and we prove it using footprint techniques, Delorme's reduction and Serre's classical bound. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_22597 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Maximum number of zeroes of polynomials on weighted projective spaces over a finite field Nardi, Jade San-José, Rodrigo Algebraic Geometry Information Theory Commutative Algebra 14G05 (Primary) 14G15, 13P10, 14G50 (Secondary) We compute the maximum number of rational points at which a homogeneous polynomial can vanish on a weighted projective space over a finite field, provided that the first weight is equal to one. This solves a conjecture by Aubry, Castryck, Ghorpade, Lachaud, O'Sullivan and Ram, which stated that a Serre-like bound holds with equality for weighted projective spaces when the first weight is one, and when considering polynomials whose degree is divisible by the least common multiple of the weights. We refine this conjecture by lifting the restriction on the degree and we prove it using footprint techniques, Delorme's reduction and Serre's classical bound. |
| title | Maximum number of zeroes of polynomials on weighted projective spaces over a finite field |
| topic | Algebraic Geometry Information Theory Commutative Algebra 14G05 (Primary) 14G15, 13P10, 14G50 (Secondary) |
| url | https://arxiv.org/abs/2507.22597 |