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arXiv · 1905.07031

Support varieties for finite tensor categories: Complexity, realization, and connectedness

Petter Andreas Bergh·Julia Yael Plavnik·Sarah Witherspoon
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Abstract

We advance support variety theory for finite tensor categories. First we show that the dimension of the support variety of an object equals the rate of growth of a minimal projective resolution as measured by the Frobenius-Perron dimension. Then we show that every conical subvariety of the support variety of the unit object may be realized as the support variety of an object. Finally, we show that the support variety of an indecomposable object is connected.

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Petter Andreas Bergh, Julia Yael Plavnik, Sarah Witherspoon. 2019-05-16. Support varieties for finite tensor categories: Complexity, realization, and connectedness. https://arxiv.org/abs/1905.07031

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