Let be a tame algebra and a directing -module (there exists no sequence of nonzero maps between indecomposable -modules for some indecomposable nonprojective -module and indecomposable direct summands of ). Then the variety of Amodules with dimension vector is a complete intersection. If, in addition, is a tilting -module then is normal.
"Geometry of decomposable directing modules over tame algebras." J. Math. Soc. Japan 54 (3) 609 - 620, July, 2002. https://doi.org/10.2969/jmsj/1191593911