# Valuative stability of polarised varieties

@article{Dervan2020ValuativeSO, title={Valuative stability of polarised varieties}, author={R. Dervan and E. Legendre}, journal={arXiv: Algebraic Geometry}, year={2020} }

Fujita and Li have given a characterisation of K-stability of a Fano variety in terms of quantities associated to valuations, which has been essential to all recent progress in the area. We introduce a notion of valuative stability for arbitrary polarised varieties, and show that it is equivalent to K-stability with respect to test configurations with integral central fibre. The numerical invariant governing valuative stability is modelled on Fujita's beta invariant, but includes a term… Expand

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