On discrete affine invariants of PL curves in Rn

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F25%3A50022648" target="_blank" >RIV/62690094:18470/25:50022648 - isvavai.cz</a>
Alternative codes found
RIV/44555601:13440/25:43899390
Result on the web
<a href="https://www.sciencedirect.com/science/article/abs/pii/S0393044025001044" target="_blank" >https://www.sciencedirect.com/science/article/abs/pii/S0393044025001044</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.geomphys.2025.105520" target="_blank" >10.1016/j.geomphys.2025.105520</a>

Result language
angličtina
Original language name
On discrete affine invariants of PL curves in Rn
Original language description
In this paper we propose and study a discrete version of affine invariants for piecewise linear curves. Each piecewise linear curve in an affine space is associated with a set of its vertices. We consider the moduli space of such curves under the action of a group of affine transformations that preserve the volume. When the natural non-degeneracy condition is satisfied, this moduli space is in one-to-one correspondence with the total space of the canonical line bundle over the Grassmannian, which is determined by the dimension of the affine space and the number of vertices of the piecewise linear curve. The space of functions on the Grassmannian is defined using the Pl & uuml;cker embedding. When the abovementioned non-degeneracy condition is satisfied, it is possible to find free generators of the algebra of functions, so that all invariants are uniquely expressed through them. We also show that the affine arc length of a smooth curve is the limit of the corresponding discrete invariant, which we call the discrete affine arc length. At the end of the paper, some low-dimensional examples are considered. (c) 2025 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics

Project
<a href="/en/project/GF24-10031K" target="_blank" >GF24-10031K: Graded differential geometry with applications</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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