All Questions
55 questions
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Number of conditions imposed by fat points to a linear system
Let $|D|$ be the linear system of degree $d$ hypersurfaces in $\mathbb{P}^n$ having multiplicity at least $m$ at $s$ general points.
Then $|kD|$ is the linear system of degree $kd$ hypersurfaces in $...
user97096
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Curves in conic bundles
Consider a smooth minimal $3$-fold conic bundle $f:X\rightarrow\mathbb{P}^2$. Then $X$ has Picard rank two and consequently also the vector space of $1$-cycles is $2$-dimensional. Then the cone of ...
- 9
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Definition of canonical pair
Let $(X,D)$ be a pair and $f:Y\rightarrow X$ a log resolution. Write
$$
K_Y + \widetilde{D} = f^{*}(K_X) + \sum_{i}a_iE_i
$$
where $\widetilde{D}$ is the strict transform of $D$. I found the following ...
- 8,998
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271
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Pseudoeffective divisors on surfaces
Consider a minimal smooth conic bundle $S$ of dimension two. Assume that there are two curves $C,F$ on $S$ such that $C^2 < 0$ and $F^2 = 0$. Let $D$ be a pseudoeffective divisor on $S$ such that $...
- 8,998
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342
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Intersections of divisors in blow-ups of $\mathbb{P}^n$
Let $p_1,p_2,p_3\in\mathbb{P}^n$ be three general points, $X$ the blow-up of $\mathbb{P}^n$ at $p_1,p_2,p_3$, then along the lines $\left\langle p_i,p_j\right\rangle$, and finally along the plane $\...
user91659