Singular curves of low degree and multifiltrations from osculating spaces

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)

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:

14 Mar 2021 09:16

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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