??? hartog fan canonical line bundle .... ???? .....

?? affine somewhat generalized toric variety with homogeneous coordinate monoid z/23 .... ???? hard to believe that toric ideal class group here is non-trivial .... ????? .....

??? hartog environment ??????? ..... ????? .......

??? "downward decorrelation" vs kummer's chemistry analogy .... ??? kummer's chemistry analogy as "downward decorrelation without a net" ???? .... ???? .... ??? explcitly getting hartog theory of nice commutative monoid .... ???? .....