Construction of set theoretic complete intersections via semigroup gluing.

*(English)*Zbl 0944.14018Summary: We present a very simple, but powerful, technique for finding monomial varieties which are set theoretic complete intersections. The technique is based on the concept of gluing semigroups that was defined by J. C. Rosales [Semigroup Forum 55, No. 2, 152-159 (1997)] and used by K. G. Fischer, W. Morris and J. Shapiro [Proc. Am. Math. Soc. 125, No. 11, 3137-3145 (1997; Zbl 0893.20047)] to characterize complete intersection affine semigroup rings. There are several techniques in the literature proving that certain varieties are set theoretic complete intersections but all of them preserve the dimension of the variety and are mainly results about curves. The technique presented here does not preserve necessarily the dimension of the variety and it can combine the known results to produce set theoretic complete intersection varieties of any dimension, see examples 4 and 5.