Invarianti proiettivi integrali inerenti a certe coppie o terne di curve chiuse

Beniamino Segre

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti (1976)

  • Volume: 61, Issue: 5, page 420-427
  • ISSN: 0392-7881

Abstract

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It is shown that, if C is a closed curve of a projective S r ( r ≥ 2 ) and Γ denotes any other closed curve lying on the developable surface Σ circumscribed to C , it is possible to attach to C and Γ a projective integral invariant, { C ; Γ } , having a simple metrical definition (given in n. 3, Cor. I). Moreover, it is proved (Theor. VII and Cor. II) that this invariant { C ; Γ } vanishes whenever Γ is semialgebraic (i.e., obtainable as the intersection of Σ with an algebraic primal of S r ) and that, if r ≥ 3 , { C ; Γ } remains unchanged when C and Γ are substituted by their projections from an arbitrary S h on an S r - h - 1 of S r skew to S h 0 ≤ h ≤ r - 3 . Further similar results are previously obtained, by using certain preliminary simple properties (cf. Theorems I and II), in connection with C , Γ and a third closed curve Δ lying on Σ .

How to cite

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Segre, Beniamino. "Invarianti proiettivi integrali inerenti a certe coppie o terne di curve chiuse." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti 61.5 (1976): 420-427. <http://eudml.org/doc/291136>.

@article{Segre1976,
author = {Segre, Beniamino},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti},
language = {ita},
month = {11},
number = {5},
pages = {420-427},
publisher = {Accademia Nazionale dei Lincei},
title = {Invarianti proiettivi integrali inerenti a certe coppie o terne di curve chiuse},
url = {http://eudml.org/doc/291136},
volume = {61},
year = {1976},
}

TY - JOUR
AU - Segre, Beniamino
TI - Invarianti proiettivi integrali inerenti a certe coppie o terne di curve chiuse
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
DA - 1976/11//
PB - Accademia Nazionale dei Lincei
VL - 61
IS - 5
SP - 420
EP - 427
LA - ita
UR - http://eudml.org/doc/291136
ER -

References

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  1. BOMPIANI, E. (1972) - Sul carattere proiettivo del rapporto plurisezionale, «Rend. Acc. Naz. Lincei», (8), 52, 150-155. Zbl0239.50011MR326557
  2. LONGO, C. (1942) - Su alcune proprietà del rapporto plurisezionale, «Rendic. di Mat.» (5)» 3 , 90-97. Zbl68.0347.03MR18843

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