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October 20, 2025Open Access

Bounding minimal log discrepancies of complexity one T-varieties

Key Points

The proof confirms the Shokurov conjecture regarding minimal log discrepancies in certain algebraic settings.
It establishes that the minimal log discrepancy is indeed bounded above by the dimension of complexity one T-varieties.
The results align with previous studies on threefolds and other types of varieties, expanding the understanding of this concept.
This work adds a significant layer to the birational classification framework for algebraic varieties.

Abstract

The minimal log discrepancy is an invariant that plays an important role in the birational classification of algebraic varieties. Shokurov conjectured that the minimal log discrepancy can always be bounded from above in terms of the dimension of the variety. We prove this conjecture for T-varieties of complexity one, adding to previous results on this conjecture which include threefolds, toric varieties, and local complete intersection varieties.

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Cite This Study

Leandro Meier (Tue,) studied this question.

synapsesocial.com/papers/68f5fcce8d54a28a75cf1a82 https://doi.org/https://doi.org/10.48550/arxiv.2503.02681

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