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Karl Schwede
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Let $X$ be a smooth degree $d$ ($d>5$) surface in $\mathbb{P}^3$. We now blow up $X$ at a point and embedd, embed it in some projective space, and and consider a projection of it into $\mathbb{P}^3$. The question is does this resulting surface have only ADE singularities? If not when is it the case? What is the degree of the final surface?

Let $X$ be a smooth degree $d$ ($d>5$) surface in $\mathbb{P}^3$. We now blow up $X$ at a point and embedd it in $\mathbb{P}^3$. The question is does this resulting surface have only ADE singularities? If not when is it the case? What is the degree of the final surface?

Let $X$ be a smooth degree $d$ ($d>5$) surface in $\mathbb{P}^3$. We now blow up $X$ at a point, embed it in some projective space, and and consider a projection of it into $\mathbb{P}^3$. The question is does this resulting surface have only ADE singularities? If not when is it the case? What is the degree of the final surface?

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Blowing up a projective surface

Let $X$ be a smooth degree $d$ ($d>5$) surface in $\mathbb{P}^3$. We now blow up $X$ at a point and embedd it in $\mathbb{P}^3$. The question is does this resulting surface have only ADE singularities? If not when is it the case? What is the degree of the final surface?