The K-polystable degenerations of divisors of bidegree (1,1,1,1) in (P^1)^4 are exactly the irreducible divisors (♥) and the new divisors (♦), and their moduli component is the blow-up of P(1,3,4,6) with weights (1,2,3).
Boozer, The moduli space of stable rank 2 parabolic bundles over an el liptic curve with 3 marked points, Proc
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K-moduli of pure states of four qubits
The K-polystable degenerations of divisors of bidegree (1,1,1,1) in (P^1)^4 are exactly the irreducible divisors (♥) and the new divisors (♦), and their moduli component is the blow-up of P(1,3,4,6) with weights (1,2,3).