ON THE DEGREE OF CURVES VANISHING AT FAT POINTS WITH EQUAL MULTIPLICITIES

ON THE DEGREE OF CURVES VANISHING AT FAT POINTS WITH EQUAL MULTIPLICITIES

The problem of determining the least degree of plane curves vanishing at given points with certain multiplicities is fascinating and difficult. In 1959,Nagata gave a conjecture on the lower bound of the degree. Since then, many mathematicians have focused on solving the conjecture for several specia...

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Veröffentlicht in:Kyushu Journal of Mathematics 2013, Vol.67(1), pp.17-27
Hauptverfasser: TU, Nguyen Chanh, HOANG, Do Trong
Format: Artikel
Sprache:eng
Schlagworte:
fat points
good subdivision
m-triangular
minimal degree
multiplicities
Nagata's conjecture
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Beschreibung
Zusammenfassung:The problem of determining the least degree of plane curves vanishing at given points with certain multiplicities is fascinating and difficult. In 1959,Nagata gave a conjecture on the lower bound of the degree. Since then, many mathematicians have focused on solving the conjecture for several special cases. In this paper, we show several results on determining the least degree for certain cases of equal multiplicities.
ISSN:1340-6116
1883-2032
DOI:10.2206/kyushujm.67.17