Assuming the non-vanishing conjecture, the abundance conjecture holds for all smooth projective varieties of numerical dimension at most one; unconditionally, it holds in dimension at most five whenever κ≥0 and ν≤1.
Birkar, Existence of log canonical flips and a special LMMP, Publ
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
fields
math.AG 1years
2025 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
Non-vanishing implies numerical dimension one abundance
Assuming the non-vanishing conjecture, the abundance conjecture holds for all smooth projective varieties of numerical dimension at most one; unconditionally, it holds in dimension at most five whenever κ≥0 and ν≤1.