817_10-11
Tangent space of \(\mathrm{Mor}(Y,X)\)¶
Goal: proof that
\[ T_{Mor(Y,x),[f]} \cong H^0(Y,\mathcal{H}om(f^*\Omega _X,\mathcal{O}_Y) \]
dimension of tangent space¶
\[ \dim T\_{Mor(Y,x),[f]} \geq h^0(Y,f^*T_X) - h^1(Y,f^*T_X) \]
Inparticular, if \(h^1(Y,f^*T_X)=0\), then smooth at \([f]\)
skip this proof.