Noether-Severi inequality and equality for irregular threefolds of general type

摘要

We prove the optimal Noether-Severi inequality that vol (X) >= 4/3 chi(omega(X)) for all smooth and irregular 3-folds X of general type over C. For those 3-folds X attaining the equality, we completely describe their canonical models and show that the topological fundamental group pi(1)(X) similar or equal to Z(2). As a corollary, we obtain for the same X another optimal inequality that vol (X) >= 4/3 h(a)(0)(X, K-X) where h(a)(0)(X, K-X) stands for the continuous rank of K-X, and we show that X attains this equality if and only if vol(X) =4/3 chi(omega(X)).

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