FanoCats

In addition to the examples linked above, here are various examples and counterexamples I have collected over time. Note that they are not all necessarily Fano!

• $\mathrm{Bl}_1\mathrm{Bl}_1\PP^2$: the double blow-up of $\PP^2$
• $\mathrm{Bl}_2\PP^n$: the blow-up of $\PP^n$ at 2 points
• Hille‒Perling’s Counterexample to King’s Conjecture
• Hirzebruch Surfaces
• Helices of exceptional collections
• Toric varieties embedding into small projective spaces