On a Problem Posed by Luigi Campedelli

Ezio Stagnaro

Bollettino dell'Unione Matematica Italiana (2011)

  • Volume: 4, Issue: 2, page 237-243
  • ISSN: 0392-4041

Abstract

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We construct an irreducible degree 10 plane curve C 10 , giving the explicit equation with real coefficients, having six [3; 3] points that are not on a conic. The fairly simple equation of C 10 enables the shape of a curve, whose equation has been researched without success since 1932, to be visualized in the real plane.

How to cite

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Stagnaro, Ezio. "On a Problem Posed by Luigi Campedelli." Bollettino dell'Unione Matematica Italiana 4.2 (2011): 237-243. <http://eudml.org/doc/290716>.

@article{Stagnaro2011,
abstract = {We construct an irreducible degree 10 plane curve $C_\{10\}$, giving the explicit equation with real coefficients, having six [3; 3] points that are not on a conic. The fairly simple equation of $C_\{10\}$ enables the shape of a curve, whose equation has been researched without success since 1932, to be visualized in the real plane.},
author = {Stagnaro, Ezio},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {6},
number = {2},
pages = {237-243},
publisher = {Unione Matematica Italiana},
title = {On a Problem Posed by Luigi Campedelli},
url = {http://eudml.org/doc/290716},
volume = {4},
year = {2011},
}

TY - JOUR
AU - Stagnaro, Ezio
TI - On a Problem Posed by Luigi Campedelli
JO - Bollettino dell'Unione Matematica Italiana
DA - 2011/6//
PB - Unione Matematica Italiana
VL - 4
IS - 2
SP - 237
EP - 243
AB - We construct an irreducible degree 10 plane curve $C_{10}$, giving the explicit equation with real coefficients, having six [3; 3] points that are not on a conic. The fairly simple equation of $C_{10}$ enables the shape of a curve, whose equation has been researched without success since 1932, to be visualized in the real plane.
LA - eng
UR - http://eudml.org/doc/290716
ER -

References

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  1. CAMPEDELLI, L., Sui piani doppi con curva di diramazione del decimo ordine, Atti. Acc. Naz. Lincei, Rendiconti, Vol. XV (1932), 358-362. 
  2. CAMPEDELLI, L., Sopra alcuni piani doppi notevoli con curva di diramazione del decimo ordine, Atti. Acc. Naz. Lincei, Rendiconti, Vol. XV (1932), 536-542. 
  3. DOLGACHEV, I., Algebraic surfaces with q = p y = 0 , Algebraic Surfaces, C.I.M.E., Cortona-Varenna 1977, Liguori ed., Napoli (1981), 97-215. MR2757651DOI10.1007/978-3-642-11087-0_3
  4. REID, M., Campedelli versus Godeaux, in ``Problems in the theory of surfaces and their classification'', (Cortona, 1988), Academic Press (1991), 309-365. MR1273384
  5. STAGNARO, E., On Campedelli branch loci, Annali Univ. Ferrara - Sez. VII - Sc. Mat., Vol. XLIII (1997), 1-26. MR1686746
  6. STAGNARO, E., What decides the existence of a branch curve? (A new Campedelli branch curve C 1 + C 9 ), to appear on ``Atti Acc. Ligure di Sc. e Lett.''. MR2808000
  7. WERNER, C., Branch curves for Campedelli double planes, Rocky Mt. J. Math.36, No. 6 (2006). 2057-2073. Zbl1143.14033MR2305646DOI10.1216/rmjm/1181069361

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