Local cohomology on a subexceptional series of representations

We consider a series of four subexceptional representations coming from the third line Freudenthal–Tits magic square; using Bourbaki notation, these are (G ? ,X) corresponding to (C 3 ,? ),(A 5 ),(D 6 ), and (E 7 ). In each case X has five G=G ×?-orbits, displaying some uniform behavior, e.g. their dimensions or defining ideals. this paper, we determine further invariants analyze uniformity within series. describe category G-equivariant coherent ???? -modules as quiver. construct explicitly simple equivariant ????-modules G-structures. ????-module structure local cohomology modules supported in orbit closures, calculate intersection groups Lyubeznik numbers. While our results for (A ),(E ) still completely uniform, displays surprisingly different which give two explanations: middle is not simply-connected, its closure Gorenstein.