Fanography

double cover of $\mathbb{P}^3$ with branch locus a divisor of degree 6

alternative

hypersurface of degree 6 in $\mathbb{P}(1,1,1,1,3)$

1. hypersurface of degree 4 in $\mathbb{P}^4$
2. double cover of 1-16 with branch locus a divisor of degree 8

complete intersection of quadric and cubic in $\mathbb{P}^5$

complete intersection of 3 quadrics in $\mathbb{P}^6$

1. section of Plücker embedding of $\mathrm{Gr}(2,5)$ by codimension 2 subspace and a quadric
2. double cover of 1-15 with branch locus an anticanonical divisor

section of half-spinor embedding of a connected component of $\mathrm{OGr}_+(5,10)$ by codimension 7 subspace

section of Plücker embedding of $\mathrm{Gr}(2,6)$ by codimension 5 subspace

section of Plücker embedding of $\mathrm{SGr}(3,6)$ by codimension 3 subspace

section of the adjoint $\mathrm{G}_2$-Grassmannian $\mathrm{G}_2\mathrm{Gr}(2,7)$ by codimension 2 subspace

zero locus of $(\bigwedge^2\mathcal{U}^\vee)^{\oplus 3}$ on $\mathrm{Gr}(3,7)$

hypersurface of degree 6 in $\mathbb{P}(1,1,1,2,3)$

double cover of $\mathbb{P}^3$ with branch locus a smooth quartic surface

alternative

hypersurface of degree 4 in $\mathbb{P}(1,1,1,1,2)$

hypersurface of degree 3 in $\mathbb{P}^4$

complete intersection of 2 quadrics in $\mathbb{P}^5$

section of Plücker embedding of $\mathrm{Gr}(2,5)$ by codimension 3 subspace

hypersurface of degree 2 in $\mathbb{P}^4$

projective space $\mathbb{P}^3$

blowup of 1-11 in an elliptic curve which is the intersection of two divisors from half the anticanonical linear system

double cover of 2-34 with branch locus a $(2,4)$-divisor

blowup of 1-12 in an elliptic curve which is the intersection of two divisors from half the anticanonical linear system

blowup of 1-17 in the intersection of two cubics

alternative

$(1,3)$-divisor on $\mathbb{P}^1\times\mathbb{P}^3$

blowup of 1-13 in a plane cubic

1. $(2,2)$-divisor on $\mathbb{P}^2\times\mathbb{P}^2$
2. double cover of 2-32 with branch locus an anticanonical divisor

blowup of 1-16 in the intersection of two divisors from $|\mathcal{O}_Q(2)|$

1. double cover of 2-35 with branch locus an anticanonical divisor such that the intersection with the exceptional divisor is smooth
2. double cover of 2-35 with branch locus an anticanonical divisor such that the intersection with the exceptional divisor is singular but reduced

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

alternative

blowup of 1-17 in a curve of degree 7 and genus 5, which is an intersection of 3 cubics

blowup of 1-14 in an elliptic curve which is an intersection of 2 hyperplanes

blowup of 1-13 in a line

intersection of 3 $(1,1)$-divisors in $\mathbb{P}^3\times\mathbb{P}^3$

alternative

blowup of 1-17 in a curve of degree 6 and genus 3 which is an intersection of 4 cubics

blowup of 1-16 in a curve of degree 6 and genus 2

blowup of 1-15 in an elliptic curve which is an intersection of 2 hyperplanes

1. blowup of 1-17 in the intersection of a quadric and a cubic where the quadric is smooth
2. blowup of 1-17 in the intersection of a quadric and a cubic where the quadric is singular but reduced

blowup of 1-14 in a conic

blowup of 1-16 in an elliptic curve of degree 5

double cover of 2-34 with branch locus a divisor of degree $(2,2)$

blowup of 1-14 in a line

blowup of 1-15 in a twisted cubic

blowup of 1-16 in a twisted quartic

blowup of 1-15 in a conic

1. blowup of 1-16 in an intersection of $A\in|\mathcal{O}_Q(1)|$ and $B\in|\mathcal{O}_Q(2)|$ such that $A$ is smooth
2. blowup of 1-16 in an intersection of $A\in|\mathcal{O}_Q(1)|$ and $B\in|\mathcal{O}_Q(2)|$ such that $A$ is singular

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

blowup of 1-17 in an elliptic curve which is an intersection of 2 quadrics

alternative

$(1,2)$-divisor on $\mathbb{P}^1\times\mathbb{P}^3$

blowup of 1-15 in a line

blowup of 1-17 in a twisted cubic

blowup of 1-17 in a plane cubic

blowup of 1-16 in a conic

blowup of 1-17 in a conic

blowup of 1-16 in a line

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

alternative

$\mathbb{P}(\mathrm{T}_{\mathbb{P}^2})$

the complete flag variety for $\mathbb{P}^2$

blowup of 1-17 in a line

$\mathbb{P}^1\times\mathbb{P}^2$

$\mathrm{Bl}_p\mathbb{P}^3$

alternative

$\mathbb{P}(\mathcal{O}_{\mathbb{P}^2}\oplus\mathcal{O}_{\mathbb{P}^2}(1))$

$\mathbb{P}(\mathcal{O}_{\mathbb{P}^2}\oplus\mathcal{O}_{\mathbb{P}^2}(2))$

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

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

blowup of the cone over a smooth quadric in $\mathbb{P}^3$ in the disjoint union of the vertex and an elliptic curve on the quadric

blowup of 3-27 in a curve of degree $(1,1,2)$

blowup of 3-19 in the proper transform of a conic through the points

blowup of 2-34 in the disjoint union of a curve of degree $(2,1)$ and a curve of degree $(1,0)$

blowup of 1-17 in the disjoint union of 3 lines

alternative

blowup of 3-27 in the tridiagonal

blowup of 2-32 in the disjoint union of a curve of degree $(0,1)$ and a curve of degree $(1,0)$

blowup of 3-27 in a curve of degree $(0,1,1)$

blowup of 3-25 in an exceptional curve of the blowup

$\mathbb{P}^1\times\mathrm{Bl}_2\mathbb{P}^2$

blowup of 3-28 in $\{x\}\times E$, $x\in\mathbb{P}^1$ and $E$ the $(-1)$-curve

blowup of 2-33 in the disjoint union of two exceptional lines of the blowup

blowup of 3-27 in a curve of degree $(1,1,3)$

blowup of 2-29 in the disjoint union of three exceptional lines of the blowup

blowup of 3-25 in the disjoint union of two exceptional lines on the same irreducible component

$\mathbb{P}^1\times\mathrm{Bl}_3\mathbb{P}^2$

$\mathbb{P}^1\times\mathrm{Bl}_4\mathbb{P}^2$

$\mathbb{P}^1\times\mathrm{Bl}_5\mathbb{P}^2$

$\mathbb{P}^1\times\mathrm{Bl}_6\mathbb{P}^2$

$\mathbb{P}^1\times\mathrm{Bl}_7\mathbb{P}^2$

$\mathbb{P}^1\times\mathrm{Bl}_8\mathbb{P}^2$