0
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185 views

Lower bound for intersection number

The base scheme is an algebraically closed field. Let $X\to \mathbf{P}^1$ be an arithmetic surface over $\mathbf{P}^1$ and let $P$ be a section of $X\to \mathbf{P}^1$. Let $D$ be an effective ...
0
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114 views

Is sum (E_i, E_j) non-positive, with E_i's the exceptional components of a desingularization

Let $Y$ be an integral normal 2-dimensional scheme and let $X\longrightarrow S$ be a flat projective morphism, where $S$ is a Dedekind scheme. Let $f:X\longrightarrow Y$ be a minimal resolution of ...
4
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1answer
709 views

intersection number

I vaguely recall the following fact that I'd like to use in my research. It should be easy to see that this holds (if it does) but I can't seem to prove it. Let $p:X\longrightarrow S$ be a (regular) ...