On discrete affine invariants of PL curves in Rn

Kód výsledku v 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>

Nalezeny alternativní kódy

RIV/44555601:13440/25:43899390

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

On discrete affine invariants of PL curves in Rn

Popis výsledku v původním jazyce

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 &amp; 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.

Název v anglickém jazyce

On discrete affine invariants of PL curves in Rn

Popis výsledku anglicky

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 &amp; 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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GF24-10031K" target="_blank" >GF24-10031K: Gradovaná diferenciální geometrie a její aplikace</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of geometry and physics

ISSN

0393-0440

e-ISSN

1879-1662

Svazek periodika

214

Číslo periodika v rámci svazku

August

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

8

Strana od-do

"Article Number: 105520"

Kód UT WoS článku

001490499100002

EID výsledku v databázi Scopus

2-s2.0-105004343696