blowup
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Problem 32：Resolution of DuVal Singularities Part 1.
Exercise: Resolve the 5 forms of DuVal Singularities (Part 1/5: $A_n$ singularities). The Minimal Model Program…
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Problem 21: Beauville II.20
Beauville Exercise II.20. Let C be curve on a smooth, projective surface S. Show that there…
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Problem 12: Hartshorne V.3.3
Hartshorne Exercise V.3.3. Let $\pi:\tilde X\ra X$ be a monoidal transformation, and let $D$ be a…
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Problem 11: Hartshorne V.3.2
Hartshorne Exercise V.3.2. Let $C$ and $D$ be curves on a surface $X$, meeting at a…
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Problem 2: Hartshorne Exercise IV.3.3 and some generalizations of Problem 1
We first make some interesting generalizations to the previous post, problem 1. Recall that we showed…
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Problem 1: Show that the blowup of $\Bbb P_k^2$ at up to 8 points can be Fano.
Define inductively a sequence of blowups $\varepsilon_n:S_n\ra S_{n-1}$, where $\varepsilon_n:S_n\ra S_{n-1}$ is the blowup of $S_{n-1}$…