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Moduli of parabolic sheaves on a polarized logarithmic scheme. (English) Zbl 1401.14063

This paper is taken from the author’s doctoral thesis, directed by A. Vistoli. It generalizes the construction of the moduli space of semistable parabolic sheaves on a smooth projective variety with an effective Cartier divisor done in [M. Maruyama and K. Yokogawa, Math. Ann. 293, No. 1, 77–99 (1992; Zbl 0735.14008)] to the case of a general projective fine saturated logarithmic scheme over a field \(k\) with a fixed global chart for the log structure and a fixed polarization. In particular, the constructed moduli stack is an Artin stack of finite type over \(k\) and it has a good (in characteristic \(0\), respectively adequate in positive characteristic) moduli space in the sense of Alper, which results to be a projective scheme. In characteristic \(0\), the author constructs also moduli spaces of parabolic sheaves withouth fixing the weights.

MSC:

14D20 Algebraic moduli problems, moduli of vector bundles
14D23 Stacks and moduli problems

Citations:

Zbl 0735.14008
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References:

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