Abstract
We study the category ๐(X, Y) generated by an exceptional pair (X, Y) in a hereditary category โ. If r = dim k Hom(X, Y) โฅ 1 we show that there are exactly 3 possible types for ๐(X, Y), all derived equivalent to the category of finite dimensional modules mod(H r ) over the r-Kronecker algebra H r . In general ๐(X, Y) will not be equivalent to a module category. More specifically, if โ is the category of coherent sheaves over a weighted projective line ๐, then ๐(X, Y) is equivalent to the category of coherent sheaves on the projective line โ1 or to mod(H r ) and, if ๐ is wild, then every r โฅ 1 can occur in this way.
ACKNOWLEDGMENTS
The second author was supported by the Polish Scientific Grant KBN 1 P03A 007 27.