I am looking for some systematic study/examples of families of projective complete intersection varieties degenerating to a projective toric variety. In particular, given a projective toric variety, when can I smoothen/deform it into a complete intersection variety? What kind of singularities are permitted for such toric varieties? A reference which deals with such questions will be very helpful.
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$\begingroup$ What is your definition of "complete intersection variety"? Do you mean a projective scheme whose local rings are each a quotient of a regular local ring by an ideal generated by a regular sequence? Or do you mean a codimension $c$ intersection of $c$ ample hypersurfaces in a projective space? $\endgroup$– Jason StarrCommented Mar 17, 2021 at 14:01
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$\begingroup$ @JasonStarr I mean the latter i.e., codimension c intersection of c ample hypersurfaces in a projective space. $\endgroup$– user45397Commented Mar 17, 2021 at 14:19
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