Large Tilting Sheaves over Weighted Noncommutative Regular Projective Curves

Let $\XX$ be a weighted noncommutative regular projective curve over a field $k$. The category $\Qcoh\XX$ of quasicoherent sheaves is a hereditary, locally noetherian Grothendieck category. We classify all tilting sheaves which have a non-coherent torsion subsheaf. In case of nonnegative orbifold Euler characteristic we classify all large (that is, non-coherent) tilting sheaves and the corresponding resolving classes. In particular we show that in the elliptic and in the tubular cases every large tilting sheaf has a well-defined slope.

2010 Mathematics Subject Classification: Primary: 14A22, 18E15, Secondary: 14H45, 14H52, 16G70

Keywords and Phrases: weighted noncommutative regular projective curve, tilting sheaf, resolving class, Prüfer sheaf, genus zero, domestic curve, tubular curve, elliptic curve, slope of quasicoherent sheaf

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