AI 中文总结
构造两个具有同构交格但雅可比关系最小度不同的九线排列，给出广义Terao猜想的反例。
AI 中文摘要
我们在复射影平面上构造了两个九线排列，它们具有同构的交格，但雅可比关系的最小度不同。共同的弱组合为 \[ (n_2,n_3,n_4)=(9,7,1), \] 因此该例子不是经典的Ziegler-Yuzvinsky对，后者的弱组合为 $(n_{2},n_{3}) = (18,6)$。对于两个定义方程 $f$ 和 $g$，我们证明 \[ {\rm mdr}(f)=4,\qquad {\rm mdr}(g)=5. \] 由于次数为 $d=9$，第一个等式给出 ${\rm mdr}(f)<d/2$。因此该对构成了广义Terao猜想的一个反例。
英文摘要
We construct two arrangements of nine lines in the complex projective plane with isomorphic intersection lattices but with different minimal degrees of Jacobian relations. The common weak combinatorics is \[ (n_2,n_3,n_4)=(9,7,1), \] so the example is not the classical Ziegler-Yuzvinsky pair, whose weak combinatorics is $(n_{2},n_{3}) = (18,6)$. For the two defining equations $f$ and $g$ we prove \[ {\rm mdr}(f)=4,\qquad {\rm mdr}(g)=5. \] Since the degree is $d=9$, the first equality gives ${\rm mdr}(f)<d/2$. Hence the pair gives a counterexample to the Generalized Terao Conjecture.
Comments7 pages, version 1.1
