Adjoints of ideals in regular local rings
Adjoints of ideals in regular local rings
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正则局部环中理想的伴随
DOI：
10.4310/mrl.1994.v1.n6.a10
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发表时间：
1994
影响因子：
1
通讯作者：
J. Lipman
中科院分区：
文献类型：
--
作者：
J. Lipman
正则局部环R中理想i的伴随是R-理想adj(I)：=H^0(Y，iomega_Y)，其中f：Y->；Spec(R)是Y非奇异且IO_Y可逆的真二元映射，omega_f是典范相对对偶化层.(这样的f应该是存在的。)基本猜想是，当n=I的解析展开式时，I.adj(i^n)=adj(i^{n+1})。这是Briancon-Skoda定理的一个强版本，包含了所有其他已知的版本。它是由H^i(Y，\omega_Y)对所有I>；0(猜想)消失而得到的。当R本质上是一个字符上的有限类型时。0场，这个消失是由Kodaira消失的Cutkosky推导出来的。当dim.R=2时，它也成立；在这种情况下，我们可以更多地讨论伴随，例如与伴随曲线和导体上的经典材料联系在一起。
The adjoint of an ideal I in a regular local ring R is the R-ideal adj(I):=H^0(Y, I\omega_Y), where f:Y -> Spec(R) is a proper birational map with Y nonsingular and IO_Y invertible, and \omega_f is a canonical relative dualizing sheaf. (Such an f is supposed to exist.) The basic conjecture is that I.adj(I^n)=adj(I^{n+1}) whenever n is >= the analytic spread of I. This is a strong version of the Briancon-Skoda theorem, implying all other known versions. It follows from the (conjectural) vanishing of H^i(Y,\omega_Y) for all i>0. When R is essentially of finite type over a char. 0 field, that vanishing has been deduced by Cutkosky from Kodaira vanishing. It also holds whenever dim.R = 2; and in this case we can say considerably more about adjoints, tying in e.g., with classical material on adjoint curves and conductors.