Chain-connected component decomposition of curves on surfaces
KONNO, Kazuhiro
J. Math. Soc. Japan, Tome 62 (2010) no. 1, p. 467-486 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
We prove that an arbitrary reducible curve on a smooth surface has an essentially unique decomposition into chain-connected curves. Using this decomposition, we give an upper bound of the geometric genus of a numerically Gorenstein surface singularity in terms of certain topological data determined by the canonical cycle. We show also that the fixed part of the canonical linear system of a 1-connected curve is always rational, that is, the first cohomology of its structure sheaf vanishes.
Publié le : 2010-04-15
Classification:  reducible curve,  singularity,  14J29,  14J17 
@article{1273236712,
     author = {KONNO, Kazuhiro},
     title = {Chain-connected component decomposition of curves on surfaces},
     journal = {J. Math. Soc. Japan},
     volume = {62},
     number = {1},
     year = {2010},
     pages = { 467-486},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1273236712}
}

KONNO, Kazuhiro. Chain-connected component decomposition of curves on surfaces. J. Math. Soc. Japan, Tome 62 (2010) no. 1, pp.  467-486. http://gdmltest.u-ga.fr/item/1273236712/