Related papers: Extracting non-canonical places

For a toric log variety with standard coefficients, we show that the minimal log discrepancy at a closed invariant point bounds the Cartier index of a neighbourhood.

Let $X$ be a complete normal variety, $B$ an effective $\mathbb{R}$-divisor on $X$, and $D$ a Cartier divisor on $X$. Assume that the pair $(X, B)$ is log terminal. We consider the problem whether $H^0(X, D) \ne 0$ and obtain some results…

Given a real curve, we study special linear systems called "very special" for which the dimension does not satisfy a Clifford type inequality. We classify all these very special linear systems when the gonality of the curve is small.

We prove a logarithmic base change theorem for pushforwards of pluri-canonical bundles and use it to deduce that positivity properties of log canonical divisors descend via smooth projective morphisms. As an application, for a surjective…

One develops {\em ab initio} the theory of rational/birational maps over reduced, but not necessarily irreducible, projective varieties in arbitrary characteristic. A numerical invariant of a rational map is introduced, called the Jacobian…

We make an observation which enables one to deduce the existence of an algebraic stack of log maps for all generalized Deligne--Faltings log structures (in particular simple normal crossings divisor) from the simplest case with log…

Let X be a smooth variety and Y a closed subscheme of X. By comparing motivic integrals on X and on a log resolution of (X,Y), we prove the following formula for the log canonical threshold of (X,Y): c(X,Y)=dim X-sup_m{(dim Y_m}/(m+1)},…

Let $X$ be a projective variety over an algebraically closed field $k$ of arbitrary characteristic $p \ge 0$. A surjective endomorphism $f$ of $X$ is $q$-polarized if $f^\ast H \sim qH$ for some ample Cartier divisor $H$ and integer $q >…

For any $n\geq 3$, we prove that there exist equivalences between these apparently unrelated objects: irreducible $n$-dimensional non degenerate projective varieties $X\subset \mathbb P^{2n+1}$ different from rational normal scrolls and…

We prove that, if X is a variety over an uncountable algebraically closed field k of characteristic zero, then any irreducible exceptional divisor E on a resolution of singularities of X which is not uniruled, belongs to the image of the…

In this paper we show that any smoothable complex projective variety, smooth in codimension two, with klt singularities and numerically trivial canonical class admits a finite cover, \'etale in codimension one, that decomposes as a product…

In this paper we prove a refined version of the canonical key formula for projective abelian schemes in the sense of Moret-Bailly, we also extend this discussion to the context of Arakelov geometry. Precisely, let $\pi: A\to S$ be a…

We compute the divisor class group and the Picard group of projective varieties with Hibi rings as homogeneous coordinate rings. These varieties are precisely the toric varieties associated to order polytopes. We use tools from the theory…

Let $V$ denote a vector space with finite positive dimension. We consider an ordered pair of linear transformations $A: V\to V$ and $A^*: V\to V$ that satisfy (i) and (ii) below. (i) There exists a basis for $V$ with respect to which the…

In this paper, we classify projective toric birational morphisms from Gorenstein toric 3-folds onto the 3-dimensional affine space with relatively ample anti-canonical divisors.

In this paper we characterize two-dimensional semi-log canonical hypersurfaces in arbitrary characteristic from the viewpoint of the initial term of the defining equation. As an application, we prove a conjecture about a uniform bound of…

We discuss a difference between the rational and the real non-vanishing conjecture for pseudo-effective log canonical divisors of log canonical pairs. We also show the log non-vanishing theorem for rationally connected varieties under…

Any sufficiently often differentiable curve in the orbit space $V/G$ of a real finite-dimensional orthogonal representation $G \to O(V)$ of a finite group $G$ admits a differentiable lift into the representation space $V$ with locally…

Let $k$ be a field, let $G$ be a reductive group, and let $V$ be a linear representation of $G$. Let $V//G = Spec(Sym(V^*))^G$ denote the geometric quotient and let $\pi: V \to V//G$ denote the quotient map. Arithmetic invariant theory…

In this paper, we study the behavior of the sets of volumes of the form $\mathrm{vol}(X,K_X+B+M)$, where $(X,B)$ is a log canonical pair, and $M$ is a nef $\mathbb{R}$-divisor. After a first analysis of some general properties, we focus on…