Related papers: The Sarkisov program on log surfaces
We prove the Sarkisov program for projective surfaces over excellent base rings, including the case of non-perfect base fields $k$ of characteristic $p>0$. We classify the Sarkisov links between Mori fibre spaces and their relations for…
We establish the minimal model program for log canonical and Q-factorial surfaces over excellent base schemes.
The purpose of this paper is two-fold. The first is to give a tutorial introduction to the Sarkisov program, a 3-dimensional generalization of Castelnuovo-N\"other Theorem ``untwisting" birational maps between Mori fiber spaces, which was…
We prove that the class of log canonical rational singularities is closed under the basic operations of the minimal model program. We also give some supplementary results on the minimal model program for log canonical surfaces.
Let (S, BS) be the log-pair associated with a compactification of a given smooth quasi-projective surface V . Under the assumption that the boundary BS is irreducible, we propose an algorithm, in the spirit of the (log) Sarkisov program, to…
In this article, we prove the Sarkisov Program for co-rank one foliations with suitable singularities on normal projective threefolds. We also exibit a weaker version of birational super-rigidity between two foliated Mori fiber spaces with…
We establish the minimal model theory for $\mathbb Q$-factorial log surfaces and log canonical surfaces in Fujiki's class $\mathcal C$.
We prove the finite generation of the adjoint ring for $\mathbb{Q}$-factorial log surfaces over any algebraically closed field.
By applying the theory of the minimal model program for adjoint foliated structures, we establish the Sarkisov program for algebraically integrable foliations on klt varieties: any two Mori fiber spaces of such structure are connected by a…
In this paper we show that any two birational Mori fiber spaces of $\Qq$-factorial gklt g-pairs are connected by a finite sequence of Sarkisov links.
We discuss the relative log minimal model theory for log surfaces in the analytic setting. More precisely, we show that the minimal model program, the abundance theorem, and the finite generation of log canonical rings hold for log pairs of…
We showed that the strong Sarkisov Program of dimension $d$ can be derived from termination of specific log flips in dimension $\leq d-1$. As a corollary, we show that the strong Sarkisov Program holds in dimension 4. Additionally, we prove…
We discuss the log minimal model theory for log surfaces. We show that the log minimal model program, the finite generation of log canonical rings, and the log abundance theorem for log surfaces hold true under assumptions weaker than the…
We prove a version of the Sarkisov program for volume preserving birational maps of Mori fibred Calabi-Yau pairs valid in all dimensions. Our theorem generalises the theorem of Usnich and Blanc on factorisations of birational maps of the…
We introduce the notion of generalized MR log canonical surfaces and establish the minimal model theory for generalized MR log canonical surfaces in full generality.
We prove a base point free theorem for nef and log big divisors on log canonical surfaces.
We discuss the birational geometry of singular surfaces in positive characteristic. More precisely, we establish the minimal model program and the abundance theorem for Q-factorial surfaces and for log canonical surfaces. Moreover, in the…
We show that a projective globally $F$-split semi-log canonical $K$-trivial surface over an algebraically closed field of characteristic $p>2$ admits an equisingular lifting over the ring of Witt vectors.
In this paper the log surfaces without $\QQ$-complement are classified. In particular, they are non-rational always. This result takes off the restriction in the theory of complements and allows one to apply it in the most wide class of log…
We work with semi-algebraic functions on arbitrary real closed fields. We generalize the notion of critical values and prove a Sard type theorem in our framework.