Related papers: A description of the sarkisov program of horospher…

Any two birational Mori fibre spaces are connected by a sequence of Sarkisov links.

In a previous work, we described the Minimal Model Program in the family of $\Qbb$-Gorenstein projective horospherical varieties, by studying certain continuous changes of moment polytopes of polarized horospherical varieties. Here, we…

We describe the Minimal Model Program in the family of $\mathbb{Q}$-Gorenstein projective horospherical varieties, by studying a family of polytopes defined from the moment polytope of a Cartier divisor of the variety we begin with. In…

For a general Fano $3$-fold of index $1$ in the weighted projective space $\mathbb{P}(1,1,1,1,2,2,3)$ we construct $2$ new birational models that are Mori fibre spaces, in the framework of the so-called Sarkisov program. We highlight a…

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…

The Sarkisov Program studies birational maps between varieties that are end products of the Minimal Model Program (MMP) on nonsingular uniruled varieties. If X and Y are terminal Q-factorial projective varieties endowed with a structure of…

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…

A subgroup H of a reductive group G is horospherical if it contains a maximal unipotent subgroup. We describe the Grothendieck semigroup of invariant subspaces of regular functions on G/H as a semigroup of convex polytopes. From this we…

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 describe the C program mori.x. It is part of PALP, a package for analyzing lattice polytopes. Its main purpose is the construction and analysis of three--dimensional smooth Calabi--Yau hypersurfaces in toric varieties. The ambient toric…

We introduce homological and homotopical $r$-syzygies of Mori fibre spaces as a generalization of Sarkisov links and relations of Sarkisov links. For any proper morphism $Y/R$, we construct a contractible (if not empty) CW complex such that…

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…

Let X \subset Proj(V) be a projective spherical G-variety, where V is a finite dimensional G-module and G = SP(2n, C). In this paper, we show that X can be deformed, by a flat deformation, to the toric variety corresponding to a convex…

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…

Suppose Gamma is an S-arithmetic subgroup of a connected, semisimple algebraic group G over a global field Q (of any characteristic). It is well known that Gamma acts by isometries on a certain CAT(0) metric space X_S that is a Cartesian…

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…

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…

Let $X$ be a smooth projective split horospherical variety over a number field $k$ and $x\in X(k)$. Contingent on Vojta's conjecture, we construct a curve $C$ through $x$ such that (in a precise sense) rational points on $C$ approximate $x$…

Due to a previous result which states that contact varieties are isomorphic to certain varieties, the momentum polytopes of contact manifolds are convex.

In this paper we describe orbits of automorphism group on a horospherical variety in terms of degrees of homogeneous with respect to natural grading locally nilpotent derivations. In case of (may be non-normal) toric varieties a description…