Type: Article

F-blowups and essential divisors for toric varieties

Chávez-Martínez, Enrique; Duarte, Daniel, Yasuda, Takehiko;

Abstract:

We investigate the relation between essential divisors and F-blowups, in particular, address the problem whether all essential divisors appear on the e-th F-blowup for large enough e. 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.