Buczyński, Jarosław; Ilten, Nathan; Ventura, Emanuele (2020). Singular curves of low degree and multifiltrations from osculating spaces. International Mathematics Research Notices, 2020(21), pp. 8139-8182. Oxford University Press 10.1093/imrn/rnaa009
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In order to study projections of smooth curves, we introduce multifiltrations obtained by combining flags of osculating spaces. We classify all configurations of singularities occurring for a projection of a smooth curve embedded by a complete linear system away from a projective linear space of dimension at most two. In particular, we determine all configurations of singularities of non-degenerate degree d rational curves in P^n when d − n ≤ 3 and d < 2n. Along the way, we describe the Schubert cycles giving rise to these projections. We also reprove a special case of the Castelnuovo bound using these multifiltrations: under the assumption d < 2n, the arithmetic genus of any nondegenerate degree d curve in P^n is at most d − n.
Item Type: |
Journal Article (Original Article) |
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Division/Institute: |
08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics |
UniBE Contributor: |
Ventura, Emanuele |
Subjects: |
500 Science > 510 Mathematics |
ISSN: |
1073-7928 |
Publisher: |
Oxford University Press |
Funders: |
[UNSPECIFIED] National Science Center, Poland ; [UNSPECIFIED] NSERC ; [UNSPECIFIED] Simons Foundation |
Projects: |
[UNSPECIFIED] "Complex contact manifolds and geometry of secants” |
Language: |
English |
Submitter: |
Sebastiano Don |
Date Deposited: |
29 Jan 2021 15:12 |
Last Modified: |
05 Dec 2022 15:45 |
Publisher DOI: |
10.1093/imrn/rnaa009 |
ArXiv ID: |
1905.11860 |
BORIS DOI: |
10.48350/151279 |
URI: |
https://boris.unibe.ch/id/eprint/151279 |
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