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Fantechi gives a few good examples in her notes and differentiates between abelian and regular cones. One can generalize her computations though: given a complete intersection ideal
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then the weights determine a grading of the ring. If we take the stacky proj, then we get a DM-stack. It should be obvious from here that there are associated sheaves from the
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This example should motivate the examples for sheaves on DM-stacks. The main geometric examples I know of are the weighted projective stacks
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860:{\displaystyle \Gamma ({\mathcal {O}}(4))=\mathbb {C} \cdot \langle x^{4},x^{3}y,x^{2}y^{2},xy^{3},y^{4},z\rangle }
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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give motivation for cone construction and applications (such as with virtual fundamental classes)
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The link for
Fantechi's lecture notes seems broken, does anyone find them anywhere else?
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346:{\displaystyle {\mathcal {O}}_{X}={\mathcal {O}}_{M}/{\mathcal {I}}}
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compute explicit examples (maybe mention macaulay2 functions...)
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action, and they are what you would expect. For example, on
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and complete intersection substacks. If we take the ring
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