Theta-regularity and log-canonical threshold

We show that an inequality, proven by Küronya-Pintye, which governs the behavior of the log-canonical threshold of an ideal over $\mathbb{P}^n$ and that of its Castelnuovo-Mumford regularity, can be applied to the setting of principally polarized abelian varieties by substituting the Castelnuovo-Mumford regularity with $Θ$-regularity of Pareschi-Popa.

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