For a given singular algebraic variety over $\mathbb{C}$, how many minimal resolutions can exist? More specifically, consider a projective quadratic cone $Q$ in $\mathbb{C}P^{4}$ (with homogeneous coordinates $x_{i},\ i=0,\ 1,\,...,\ 4$), given by single equation: $x_{0}x_{3}-x_{1}x_{2} = 0.$ The only singular point of $Q$ has coordinates $[0:0:0:0:1].$ Is there any way to study minimal resolutions of this cone? Especially I am interested in the relation of Thom's complex cobordism class of minimal resolution and the ambient one in this case.
2026-03-25 05:07:05.1774415225
Minimal resolutions of singularities in higher dimensions and their cobordism class.
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