Eric Sharpe - Examples of homological projective duality in physics

When is a matrix factorization `pointlike’?
One necessary condition:
contractible off a pointlike locus.
W = xy
x
O
O
y
Example: C 2
is contractible on {y ≠ 0} :
There exist maps s, t s.t. 1 = ys + tx
namely t = 0 , s = y −1
X =
{x ≠ 0}
Sim’ly, contractible on
hence support lies on {x = y = 0}