F-blowups and essential divisors for toric varieties
Abstract
We investigate the relation between essential divisors and F-blowups, in particular, address the problem whether all essential divisors appear on the -th F-blowup for large enough . Focusing on the case of normal affine toric varieties, we establish a simple sufficient condition for a divisor over the given toric variety to appear on the normalized limit F-blowup as a prime divisor. As a corollary, we show that if a normal toric variety has a crepant resolution, then the above problem has a positive answer, provided that we use the notion of essential divisors in the sense of Bouvier and Gonzalez-Sprinberg. We also provide an example of toric threefold singularities for which a non-essential divisor appears on an F-blowup.
Keywords
Cite
@article{arxiv.2304.13247,
title = {F-blowups and essential divisors for toric varieties},
author = {Enrique Chávez-Martínez and Daniel Duarte and Takehiko Yasuda},
journal= {arXiv preprint arXiv:2304.13247},
year = {2024}
}
Comments
24 pages. v2: minor revision, v3: fixed errors that was pointed out by a referee and based on confusion about several notions of essential divisors, v4: modified the definition of ciritical arrows, added some descriptions to help understanding of the discussion