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A Nonvanishing Theorem for Q-divisors
Jungkai Alfred Chen, Meng Chen, De-Qi Zhang
We prove a non-vanishing theorem of the cohomology H^0 of the adjoint divisor K_X + L' where L' is the round up of a nef and big Q-divisor L.
A sharp lower bound for the canonical volume of 3-folds of general type
Meng Chen
Let V be a smooth projective 3-fold of general type. Denote by , a rational number, the self-intersection of the canonical sheaf of any minimal model of V. One defines a…
Minimal threefolds with small slope and the Noether inequality for canonically polarized threefolds
Meng Chen
1) We give a 3-dimensional analogue of M. Noether's inequality for canonically polarized threefolds: . This inequality is sharp by known examples of M. Kobayash…
Canonical stability of 3-folds of general type with
Meng Chen
We study the canonical stability of a smooth projective 3-fold of general type. We prove that (1) gives a birational map onto its image provided the geometric genus $p…
The relative pluricanonical stability for 3-folds of general type
Meng Chen
This paper aims to improve a theorem of Janos Kollar. For a given Complex projective threefold X of general type, suppose the plurigenus p_k(X)\ge 2, Kollar proved that the (11k+5)…