= Unavoidable support at a non-Cartier point
If a <Weil divisor> $D$ on a <normal variety> is not Cartier at $x$, every linearly equivalent divisor has $x$ in its <support of a Weil divisor>. Otherwise that representative would vanish near $x$, expressing $D$ as a <principal Weil divisor> there. On $V(ac-b^2)$ the prime divisor $V(a,b)$ is not Cartier at the origin: its ideal has two independent generators modulo the <maximal ideal> times that ideal. This gives an unavoidable support point even for representatives with negative coefficients.
Back to article page
