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Projectivity of good moduli spaces of vector bundles on stacky curves

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EMGW05 - Moduli stacks and enumerative geometry

An application of the Existence Theorem for good moduli spaces shows that the moduli stack of semistable vector bundles on a stacky curve has a proper good moduli space. In this talk we will show that this moduli space is in fact a projective variety, by constructing a line bundle on the stack and showing that it has enough sections. We will also discuss how to relate moduli stacks of semistable parabolic bundles to moduli stacks of vector bundles on stacky curves.

This talk is part of the Isaac Newton Institute Seminar Series series.

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