Related papers: An abundance theorem for generalised pairs
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 canonicity and normalization for dependent type theory with a cumulative sequence of universes and a type of Boolean. The argument follows the usual notion of reducibility, going back to Godel's Dialectica interpretation and 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 discuss the minimal model program for b-log varieties, which is a pair of a variety and a b-divisor, as a natural generalization of the minimal model program for ordinary log varieties. We show that the main theorems of the log MMP work…
Given an NQC log canonical generalized pair $(X,B+M)$ whose underlying variety $X$ is not necessarily $\mathbb{Q}$-factorial, we show that one may run a $(K_X+B+M)$-MMP with scaling of an ample divisor which terminates, provided that…
This paper generalizes Shelah's generic pair conjecture (now theorem) for the measurable cardinal case from first order theories to finite diagrams. We use homogeneous models in the place of saturated models.
We show the finiteness of log pluricanonical representations under the assumption of the existence of a good minimal model.
We establish a Koll\'ar-type gluing theory for NQC generalized log canonical pairs and use it to prove semi-ampleness results of NQC generalized pairs. As consequences, we prove the existence of flips for any NQC generalized log canonical…
We show that minimal models of $\mathbb{Q}$-factorial NQC log canonical generalised pairs exist, assuming the existence of minimal models of smooth varieties. More generally, we prove that on a $\mathbb{Q}$-factorial NQC log canonical…
We show the existence of $n$-complements for generalized pairs with additional Diophantine approximation properties when the coefficients of boundaries belong to a DCC set.
In this note we prove that the factorization theorem for dominated polynomials previously proved by the authors is equivalent to an alternative factorization scheme that uses classical linear techniques and a linearization process. However,…
The purpose of this paper is to give two applications of Fourier transforms and generic vanishing theorems: - we give a cohomological characterization of principal polarizations - we prove that if $X$ an abelian variety and $\Theta $ a…
We provide a semi-grammatical description of the set of normal proofs of positive formulae in minimal predicate logic, i.e. a grammar that generates a set of schemes, from each of which we can produce a finite number of normal proofs. This…
We prove that the canonical ring of a smooth projective variety is finitely generated.
This paper is a companion article to our previous paper (J. Stat. Phys. 119, 1283 (2005), cond-mat/0408681), which introduced a generalized canonical ensemble obtained by multiplying the usual Boltzmann weight factor $e^{-\beta H}$ of the…
This paper is concerned with structures of general graphs with perfect matchings. We first reveal a partially ordered structure among factor-components of general graphs with perfect matchings. Our second result is a generalization of…
It is shown that in equilibrium a canonical ensemble of particles with two-particle interaction the Gibbs distribution function may be expressed uniquely through a pair distribution function. It means, that for given values of the particle…
We prove the theorems which are equivalent to the Roland's results such that a new form of them allows to consider some generalizations. In particular, we give generators of primes more than a fixed prime.
We prove a Ramsey theorem for finite sets equipped with a partial order and a fixed number of linear orders extending the partial order. This is a common generalization of two recent Ramsey theorems due to Soki\'c. As a bonus, our proof…
We prove the abundance conjecture for projective slc surfaces over arbitrary fields of positive characteristic. The proof relies on abundance for lc surfaces over abritrary fields, proved by Tanaka, and on the technique of Hacon and Xu to…