Abstract
We show that the Segre product of a line and a smooth conic, naturally embedded in P5, is a smooth projective surface of tame representation type, namely all continuous families of indecomposable ACM bundles have dimension one. To our knowledge, this is the first example of smooth projective variety of this kind, besides the elliptic curve, which is of tame representation type according to Atiyah (1957).
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