Fanography

double cover of 3-27 with branch locus a divisor of degree $(2,2,2)$

divisor from $|\mathcal{L}^{\otimes 2}\otimes\mathcal{O}(2,3)|$ on the $\mathbb{P}^2$-bundle $\mathbb{P}(\mathcal{O}\oplus\mathcal{O}(-1,-1)^{\oplus 2})$ over $\mathbb{P}^1\times\mathbb{P}^1$ such that $X\cap Y$ is irreducible, and $\mathcal{L}$ is the tautological bundle, and $Y\in|\mathcal{L}|$

divisor on $\mathbb{P}^1\times\mathbb{P}^1\times\mathbb{P}^2$ of degree $(1,1,2)$

blowup of 2-18 in a smooth fiber of the composition of the projection to $\mathbb{P}^1\times\mathbb{P}^2$ with the projection to $\mathbb{P}^2$ of the double cover with the projection

blowup of 2-34 in a curve $C$ of degree $(5,2)$ such that $C\hookrightarrow\mathbb{P}^1\times\mathbb{P}^2\to\mathbb{P}^2$ is an embedding

blowup of 1-17 in the disjoint union of a line and an elliptic curve of degree 4

alternative

complete intersection of degree $(1,0,2)$ and $(0,1,1)$ in $\mathbb{P}^1\times\mathbb{P}^1\times\mathbb{P}^3$

blowup of 2-32 in an elliptic curve which is the intersection of two divisors from $|-\frac{1}{2}\mathrm{K}_W|$

divisor from the linear system $|(\alpha\circ\pi_1)^*(\mathcal{O}_{\mathbb{P}^2}(1)\otimes\pi_2^*(\mathcal{O}_{\mathbb{P}^2}(2))|$ where $\pi_i\colon\mathrm{Bl}_1\mathbb{P}^2\times\mathbb{P}^2\to\mathrm{Bl}_1\mathbb{P}^2,\mathbb{P}^2$ are the projections, and $\alpha\colon\mathrm{Bl}_1\mathbb{P}^2\to\mathbb{P}^2$ is the blowup

blowup of the cone over the Veronese of $\mathbb{P}^2$ in $\mathbb{P}^5$ with center the disjoint union of the vertex and a quartic curve on $\mathbb{P}^2$

blowup of 1-16 in the disjoint union of 2 conics

alternative

complete intersection of degree $(1,0,1)$, $(0,1,1)$ and $(0,0,2)$ in $\mathbb{P}^1\times\mathbb{P}^1\times\mathbb{P}^4$

blowup of 2-35 in an elliptic curve which is the intersection of two divisors from $|-\frac{1}{2}\mathrm{K}_{V_7}|$

blowup of 1-17 in the disjoint union of a line and a twisted cubic

blowup of 2-32 in a curve $C$ of bidegree $(2,2)$ such that the composition $C\hookrightarrow W\hookrightarrow\mathbb{P}^2\times\mathbb{P}^2\overset{p_i}{\to}\mathbb{P}^2$ is an embedding for $i=1,2$

blowup of 1-17 in the disjoint union of a plane cubic curve and a point outside the plane

blowup of 1-16 in the disjoint union of a line and a conic

blowup of 2-35 in the proper transform of a twisted cubic containing the center of the blowup

divisor on $\mathbb{P}^1\times\mathbb{P}^1\times\mathbb{P}^2$ of degree $(1,1,1)$

blowup of 1-17 in the disjoint union of a line and a conic

blowup of 1-16 in two non-collinear points

blowup of 1-16 in the disjoint union of two lines

blowup of 2-34 in a curve of degree $(2,1)$

blowup of 2-34 in a conic on $\{x\}\times\mathbb{P}^2$, $x\in\mathbb{P}^1$

blowup of 2-35 in the proper transform of a conic containing the center of the blowup

the fiber product of 2-32 with $\mathrm{Bl}_p\mathbb{P}^2$ over $\mathbb{P}^2$

alternative

complete intersection of degree $(1,1,0)$ and $(0,1,1)$ in $\mathbb{P}^1\times\mathbb{P}^2\times\mathbb{P}^2$

blowup of 1-17 in the disjoint union of two lines

alternative

$\mathbb{P}(\mathcal{O}(1,0)\oplus\mathcal{O}(0,1))$ over $\mathbb{P}^1\times\mathbb{P}^1$

blowup of 1-17 in the disjoint union of a point and a line

alternative

blowup of line on a plane which is section of 2-34 mapping to $\mathbb{P}^2$

$\mathbb{P}^1\times\mathbb{P}^1\times\mathbb{P}^1$

$\mathbb{P}^1\times\mathrm{Bl}_p\mathbb{P}^2$

blowup of 2-35 in a line on the exceptional divisor

blowup of 2-35 in the proper transform of a line containing the center of the blowup

alternative

$\mathbb{P}_{\mathbb{F}_1}(\mathcal{O}\oplus\mathcal{O}(\ell))$ where $\ell^2=1$

blowup of the cone over a smooth quadric in $\mathbb{P}^3$ in the vertex

alternative

$\mathbb{P}(\mathcal{O}\oplus\mathcal{O}(1,1))$ over $\mathbb{P}^1\times\mathbb{P}^1$