M ¯ 0 , n is not a Mori dream space
M ¯ 0 , n is not a Mori dream space
Building on the work of Goto, Nishida, and Watanabe on symbolic Rees algebras of monomial primes, we prove that the moduli space of stable rational curves with n punctures is not a Mori dream space for n > 133 . This answers a question posed by Hu and Keel.