{'fraction_non_alphanumeric': 0.008021390374331552, 'fraction_numerical': 0.00267379679144385, 'mean_word_length': 4.769230769230769, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
STABILITY COMPUTATION VIA GROBNER BASIS

In this article, we discuss a Grobner basis algorithm related to the stability of algebraic varieties in the sense of Geometric Invariant Theory. We implement the algorithm with Macaulay 2 and use it to prove the stability of certain curves that play an important role in the log minimal model program for the moduli space of curves.