Effective Behavior on Multiple Linear Systems
Asian J. Math., Tome 8 (2004) no. 1, p. 287-304 / Harvested from Project Euclid
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It is a fundamental problem in algebraic geometry to understand the behavior of a multiple linear system |nD| on a projective complex manifold X for large n. For example, the well-known Riemann-Roch problem is to compute the function n ↦ h0(OX(nD)) := dimC H0(X,OX(nD)). In the introduction to his collected works [33], Zariski cited the Riemann-Roch problem as one of the four "difficult unsolved questions concerning projective varieties (even algebraic surfaces)". The other natural problems about |nD| are to find the fixed part and base points (see [32]), the very ampleness, the properties of the associated rational map and its image variety, the finite generation of the ring of sections. ¶ For a genus g curve X, Riemann-Roch theorem gives good and effective solutions to these problems.
Publié le : 2004-01-14
Classification:  
@article{1088090062,
     author = {Tan
, Sheng-Li},
     title = {Effective Behavior on Multiple Linear Systems},
     journal = {Asian J. Math.},
     volume = {8},
     number = {1},
     year = {2004},
     pages = { 287-304},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1088090062}
}

Tan
, Sheng-Li. Effective Behavior on Multiple Linear Systems. Asian J. Math., Tome 8 (2004) no. 1, pp.  287-304. http://gdmltest.u-ga.fr/item/1088090062/