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A Note on the Effective Non-vanishing Conjecture
Qihong Xie
We give a reduction of the irregular case for the effective non-vanishing conjecture by virtue of the Fourier-Mukai transform. As a consequence, we reprove that the effective non-v…
Effective Non-vanishing for Algebraic Surfaces in Positive Characteristic
Qihong Xie
We give a theorem on the effective non-vanishing problem for algebraic surfaces in positive characteristic. For the Kawamata-Viehweg vanishing, the logarithmic Kollar vanishing and…
The Nef Curve Cone Theorem Revisited
Qihong Xie
We revisit the nef curve cone theorem and use it to reprove the pseudo-effectivity of the second Chern classes for terminal weak Q-Fano varieties.
On Effective Non-vanishing of Weil Divisors on Algebraic Surfaces
Qihong Xie
We give a counterexample and some conclusions for effective non-vanishing of Weil divisors on algebraic surfaces.
On Pseudo-Effectivity of the Second Chern Classes for Smooth Threefolds
Qihong Xie
We prove that for smooth projective threefolds whose anticanonical divisors are nef, the second Chern classes are pseudo-effective under a weak assumption. As an application, the p…