curves
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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 20: Hartshorne IV.1.6
Hartshorne Exercise IV.1.6. Let $X$ be a curve of genus $g$. Show that there is a…
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Problem 19: Hartshorne IV.1.5
Hartshorne Exercise IV.1.5. For an effective divisor $D$ on a curve $X$ of genus $g$, show…
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Problem 18: Hartshorne IV.1.3
Hartshorne Exercise IV.1.3. Let $X$ be an integral, separated, regular, one-dimensional scheme of finite type over…
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Problem 17: Hartshorne IV.1.2
Hartshorne Exercise IV.1.2. Again let $X$ be a curve, and let $P_1,…,P_r\in X$ be points. Then…
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Problem 16: Hartshorne IV.1.1
Hartshorne Exercise V.1.1. Let $X$ be a curve, and let $P\in X$ be a point. Then…
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Problem 6: Hartshorne IV.3.3
Hartshorne Exercise IV.3.3. Let $X$ be a plane curve of degree 4. (a) Show that the…
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Problem 5: Hartshorne IV.3.1
Hartshorne Exercise IV.3.7. If $X$ is a curve of genus 2, show that a divisor $D$…
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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…