论文标题
部分可观测时空混沌系统的无模型预测
Twisted logarithmic complexes of positively weighted homogeneous divisors
论文作者
论文摘要
对于第1等级的本地系统，在复杂的歧管$ x $上减少的除数的补充中，其协同学是由扭曲的Meromorormorormorormormorormormorormormorormormorormormorormormorormormorormorormormorormorormormorormorology计算出来的。假设除数到处都是均匀加权的同质性，那么我们通过使用更强大的版本的相关复合物（$ d_x $ -modules的相关复合物）来研究其扭曲的对数子复合（LCT）的必要条件，称为对数比较定理（LCT）。 In case the connection is a pullback by a defining function $f$ of the divisor and the residue is $α$, we prove among others that if LCT holds, the annihilator of $f^{α-1}$ in $D_X$ is generated by first order differential operators and $α-1-j$ is not a root of the Bernstein-Sato polynomial for any positive integer $j$.相反的情况下，假设这两个条件中的任何一个，以防$ d_x $ - 模块的相关复合物除外，除了顶级。在局部系统恒定的情况下，除数由均匀的多项式定义，并且相关的投射性超表面仅具有加权的均质孤立奇异性，我们表明LCT等同于$ -1 $是bernstein-sato polynomial的独特整体根。在适当的假设对残基的假设下，我们还提供了简单的LCT证明，这是与Castelnuovo-Mummord的规律性相关的较高共同体学的立即推论。在这里，还处理了零延伸案例。
For a rank 1 local system on the complement of a reduced divisor on a complex manifold $X$, its cohomology is calculated by the twisted meromorphic de Rham complex. Assuming the divisor is everywhere positively weighted homogeneous, we study necessary or sufficient conditions for a quasi-isomorphism from its twisted logarithmic subcomplex, called the logarithmic comparison theorem (LCT), by using a stronger version in terms of the associated complex of $D_X$-modules. In case the connection is a pullback by a defining function $f$ of the divisor and the residue is $α$, we prove among others that if LCT holds, the annihilator of $f^{α-1}$ in $D_X$ is generated by first order differential operators and $α-1-j$ is not a root of the Bernstein-Sato polynomial for any positive integer $j$. The converse holds assuming either of the two conditions in case the associated complex of $D_X$-modules is acyclic except for the top degree. In the case where the local system is constant, the divisor is defined by a homogeneous polynomial, and the associated projective hypersurface has only weighted homogeneous isolated singularities, we show that LCT is equivalent to that $-1$ is the unique integral root of the Bernstein-Sato polynomial. We also give a simple proof of LCT in the hyperplane arrangement case under appropriate assumptions on residues, which is an immediate corollary of higher cohomology vanishing associated with Castelnuovo-Mumford regularity. Here the zero-extension case is also treated.
