TY - JOUR
T1 - Kawachi's invariant for fat points
AU - Hara, Nobuo
N1 - Copyright:
Copyright 2005 Elsevier Science B.V., Amsterdam. All rights reserved.
PY - 2001/12/7
Y1 - 2001/12/7
N2 - We extend Kawachi's invariant for reduced points on a normal suface to an invariant defined for possibly non-reduced zero-dimensional closed subschemes (or fat points) on a surface with rational singularities. We give an upper bound of this invariant in terms of the length of the fat point and the discrepancy of the minimal resolution. As an application we prove a Reider-type theorem for k-very ampleness on surfaces with rational singularities.
AB - We extend Kawachi's invariant for reduced points on a normal suface to an invariant defined for possibly non-reduced zero-dimensional closed subschemes (or fat points) on a surface with rational singularities. We give an upper bound of this invariant in terms of the length of the fat point and the discrepancy of the minimal resolution. As an application we prove a Reider-type theorem for k-very ampleness on surfaces with rational singularities.
KW - 14C20
KW - 14F17
KW - 14J17
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U2 - 10.1016/S0022-4049(00)00188-2
DO - 10.1016/S0022-4049(00)00188-2
M3 - Article
AN - SCOPUS:0041867603
VL - 165
SP - 201
EP - 211
JO - Journal of Pure and Applied Algebra
JF - Journal of Pure and Applied Algebra
SN - 0022-4049
IS - 2
ER -