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Let $X$ be a algebraic surface, $\Lambda$ be a linear system, and $p\in \Lambda$ be its base point. We blow up $X$ at $p$, denote the exceptional curve $E$.

Q: For any $C\in|\Lambda|$, can we say $(\sigma^*(C)-m_p(E))(\sigma^*(C)-m_p(E))\geq0$, where $\sigma$ denotes the blow up process, $m_p$ means the multiple number at $p$, and $E$ denotes the exceptional curve?

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    $\sigma^*(C)^2=C^2$. – 2017-02-18
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    @Mohan So sorry, I made a mistake, please see the modified question. – 2017-02-19
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    Bad notation. If you meant $m_p(C)E$, this is correct for a general curve $C\in|\Lambda|$. – 2017-02-19

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