Data di Pubblicazione:
2021
Citazione:
A geometric characterization of toric singularities / J. Moraga, R. Svaldi. - (2021 Aug 03). [10.48550/arXiv.2108.01717]
Abstract:
Given a projective contraction $\pi \colon X\rightarrow Z$ and a log canonical pair $(X, B)$ such that $-(K_X+B)$ is nef over a neighborhood of a closed point $z\in Z$, one can define an invariant, the complexity of $(X, B)$ over $z \in Z$, comparing the dimension of $X$ and the relative Picard number of $X/Z$ with the sum of the coefficients of those components of $B$ intersecting the fibre over $z$. We prove that the complexity of $(X,B)$ over $z\in Z$ is non-negative and that when it is zero then $(X,\lfloor B \rfloor) \rightarrow Z$ is formally isomorphic to a morphism of toric varieties around $z\in Z$. In particular, considering the case when $\pi$ is the identity morphism, we get a geometric characterization of singularities that are formally isomorphic to toric singularities. This gives a positive answer to a conjecture due to Shokurov.
Tipologia IRIS:
24 - Pre-print
Elenco autori:
J. Moraga, R. Svaldi
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