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Reduction type of non-hyperelliptic genus 3 curves
| hal.structure.identifier | Institut de Recherche Mathématique de Rennes [IRMAR] | |
| dc.contributor.author | LERCIER, Reynald | |
| hal.structure.identifier | Équipe Théorie des Nombres | |
| dc.contributor.author | LIU, Qing | |
| hal.structure.identifier | Institut de Recherche Mathématique de Rennes [IRMAR] | |
| dc.contributor.author | LORENZO GARCÍA, Elisa | |
| hal.structure.identifier | Institut de Mathématiques de Marseille [I2M] | |
| hal.structure.identifier | Institut de Recherche Mathématique de Rennes [IRMAR] | |
| dc.contributor.author | RITZENTHALER, Christophe | |
| dc.date | 2021 | |
| dc.date.accessioned | 2024-04-04T03:06:19Z | |
| dc.date.available | 2024-04-04T03:06:19Z | |
| dc.date.created | 2018-03 | |
| dc.date.issued | 2021 | |
| dc.identifier.issn | 1937-0652 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/193324 | |
| dc.description.abstractEn | Let $C/K$ be a smooth plane quartic over a discrete valuation field. We give a characterization of the type of reduction (ie smooth plane quartic, hyperelliptic genus 3 curve or bad) over $K$ in terms of the existence of a special plane quartic model and, over $\bar{K}$, in terms of the valuations of the Dixmier-Ohno invariants of $C$ (if the characteristic of the residue field is not $2,\,3,\,5$ or $7$). When the reduction is (potentially) good we also provide an equation for the special fiber of a generic quartic. On the way, we gather general results on geometric invariant theory over an arbitrary ring $R$ in the spirit of {Seshadri 1977}. For instance when $R$ is a discrete valuation ring, we show the existence of a homogeneous system of parameters over $R$ and we exhibit precise ones for ternary quartic forms under the action of $SL_{3,R}$ depending only on the characteristic of the residue field. | |
| dc.description.sponsorship | Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation - ANR-11-LABX-0020 | |
| dc.language.iso | en | |
| dc.publisher | Mathematical Sciences Publishers | |
| dc.subject.en | invariants | |
| dc.subject.en | hyperelliptic | |
| dc.subject.en | valuation | |
| dc.subject.en | smooth plane quartic | |
| dc.subject.en | reduction | |
| dc.title.en | Reduction type of non-hyperelliptic genus 3 curves | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
| dc.subject.hal | Mathématiques [math]/Géométrie algébrique [math.AG] | |
| dc.identifier.arxiv | 1803.05816 | |
| bordeaux.journal | Algebra & Number Theory | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01762200 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01762200v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Algebra%20&%20Number%20Theory&rft.date=2021&rft.eissn=1937-0652&rft.issn=1937-0652&rft.au=LERCIER,%20Reynald&LIU,%20Qing&LORENZO%20GARC%C3%8DA,%20Elisa&RITZENTHALER,%20Christophe&rft.genre=article |
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