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Results tagged with reference-request
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user 8621
This tag is used if a reference is needed in a paper or textbook on a specific result.
5
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0
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Syzygies of the singular locus of a nodal plane curve
Let $C\subset \mathbb{P}^2$ be a reduced nodal complex plane curve of degree $d$. Let $\Sigma$ be the set of nodes of $C$, and let $I$ be the ideal of $\Sigma$. Denote with $S=\mathbb{C}[x,y,z]$ the p …
- 3,338
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Where can I find the divisor class groups of du Val singularities?
You can mimic the quadric cone construction (if I did not make any mistakes in my computation).
An $A_{2k-1}$ singularity is the vertex of the cone $S$ given by $x^2+y^2+z^{2k}=0$ in the weighted pro …
- 3,338
5
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Cohomology of complete intersections
If $X$ is smooth then Lefschetz' hyperplane theorem and Poincaré duality yield that $H^i(X,\mathbb{Z})=H^i(\mathbb{P}^n,\mathbb{Z})$ for $i=0,\dots, 2\dim X$, $i\neq \dim X$.
(This is proven in Dimca' …
- 3,338
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Does there exist a holomorphic fibration of genus two over $\mathbb{P}^{1}$ with $7$ nodal s...
Let $S$ be the product $C\times \mathbb{P}^1$, with $C$ a genus two curve. Take points $p_1,\dots,p_7\in S$ in seven distinct fibers. Now blow-up $S$ in the points $p_1,\dots,p_7$. Then the induced fi …
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