-PURITY VERSUS LOG CANONICITY FOR POLYNOMIALS
In this article, we consider the conjectured relationship between $F$-purity and log canonicity for polynomials over $\mathbb{C}$. In particular, we show that log canonicity corresponds to dense $F$-pure type for all polynomials whose supporting monomials satisfy a certain nondegeneracy condition. We also show that log canonicity corresponds to dense $F$-pure type for very general polynomials over $\mathbb{C}$. Our methods rely on showing that the $F$-pure and log canonical thresholds agree for infinitely many primes, and we accomplish this by comparing these thresholds with the thresholds associated to their monomial term ideals.
2013 ◽
Vol 149
(9)
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pp. 1495-1510
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2015 ◽
Vol 366
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pp. 101-120
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2003 ◽
Vol 85
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pp. 30-49
1973 ◽
Vol 50
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pp. 1194-1215
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2015 ◽
Vol 25
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pp. 1530030
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1967 ◽
Vol 5
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pp. 375-379
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2001 ◽
Vol 269
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pp. 317-361
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2010 ◽
Vol 34
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pp. 53-67
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