For the ideal I generated by the 2-minors of the matrix {{x^7, y^2, z}, {y^11, z, x^10}}, the extended symbolic Rees ring is Noetherian if and only if the field has characteristic 2 or 3.
Ebina , Master theses, Meiji University 2017 (Japanese)
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Infinitely generated symbolic Rees rings of positive characteristic
For the ideal I generated by the 2-minors of the matrix {{x^7, y^2, z}, {y^11, z, x^10}}, the extended symbolic Rees ring is Noetherian if and only if the field has characteristic 2 or 3.