11 citations · 12 across the 7 of their papers we have counts for
8 papers
Generalised Cone Conjecture, III: Non-generic Sakai surfaces
Vladimir Lazić, Isabel Stenger, Zhixin Xie
We show that no meaningful version of the Cone Conjecture holds for non-generic Sakai surfaces.
Generalised Cone Conjecture, II: Generic Sakai surfaces
Vladimir Lazić, Isabel Stenger, Zhixin Xie
In this paper we prove that the Generalised Cone Conjecture holds for generic Sakai surfaces, which completes the proof of the Generalised Cone Conjecture in dimension two. Further…
Generalised Cone Conjecture, I: Beyond Calabi--Yau
Vladimir Lazić, Isabel Stenger, Zhixin Xie
This is the first of two papers in which we prove the Generalised Cone Conjecture on surfaces.
Nakayama-Zariski decomposition and the termination of flips
Vladimir Lazić, Zhixin Xie
We show that for pseudoeffective projective pairs the termination of one sequence of flips implies the termination of all flips, assuming a natural conjecture on the behaviour of t…
Cones of divisors on blown up at eight very general points
Isabel Stenger, Zhixin Xie
Let be the blowup of at eight very general points. We give a complete description of its nef and effective cones. Moreover, we show that there exists a rational…
Rationally connected threefolds with nef and bad anticanonical divisor, II
Zhixin Xie
Let be a smooth complex projective rationally connected threefold with nef and not semi-ample. In our previous work, we classified all such threefolds when ha…
The Nonvanishing problem for varieties with nef anticanonical bundle
Vladimir Lazić, Shin-ichi Matsumura, Thomas Peternell +2
We prove that if is a threefold pair with mild singularities such that is nef, then the numerical class of is effective.
Anticanonical geometry of the blow-up of in points and its Fano model
Zhixin Xie
Building on the work of Casagrande-Codogni-Fanelli, we develop our study on the birational geometry of the Fano fourfold which is the moduli space of semi-stable ran…