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4
votes
Automorphisms and infinitesimal deformations of a smooth complete intersection
I can suggest you a shorthand for your second question, in case you need a practical answer.
First, if $X$ is a smooth complete intersection, let me denote by $A_X$ the affine cone over it, by $U_X= A …
0
votes
Sections of a sheaf of differentials on a weighted complete intersection
Theorem 0.2 here (On stability of tangent bundles of Fano manifolds with b2 = 1) gives a excellent survey on vanishings. In particular if, as you ask, $q<dim \ X$, then the vanishing properties for $H …