Related papers: Arithmetic linear series with base conditions

In this paper, we establish the Zariski decompositions of arithmetic R-divisors of continuous type on arithmetic surfaces and investigate several properties. We also develop the general theory of arithmetic R-divisors on arithmetic…

We introduce and study the restricted volume of a divisor along a subvariety. Our main result is a description of the irreducible components of the augmented base locus by the vanishing of the restricted volume.

The purpose of this paper is to investigate the behaviour of certain asymptotic invariants of line bundles on projective surfaces. In particular, we describe the volume of line bundles and their destabilizing numbers.

We give an example that the volume of an $\mathbb{R}$-divisor on a family of complex smooth surfaces jumps at infinite many prime divisors in the base. Our example follows the construction in \cite{1}.

We discuss different generalizations of Zariski decomposition, relations between them and connections with finite generation of divisorial algebras.

In this article, we generalize several fundamental results for arithmetic divisors, such as the continuity of the volume function, the generalized Hodge index theorem, Fujita's approximation theorem for arithmetic divisors and Zariski…

We give a relation between the existence of a Zariski decomposition and the behavior of the restricted volume of a big divisor on a smooth (complex) projective variety. Moreover, we give an analytic description of the restricted volume in…

In this note, we observe several properties of arithmetic divisors on the projective line over Z and give their Zariski decompositions.

It is known how to compute the Zariski closure of a finitely generated monoid of matrices and, more generally, of a set of matrices specified by a regular language. This result was recently used to give a procedure to compute all polynomial…

We consider linear systems on toric varieties of any dimension, with invariant base points, giving a characterization of special linear systems. We then make a new conjecture for linear systems on rational surfaces.

This is a survey on the finite basis problem for varieties of algebraic systems. Our exposition is in two directions: (i) We give numerous examples of varieties which are not finitely based. (ii) We give examples of important varieties with…

In a 1962 paper, Zariski introduced the decomposition theory that now bears his name. Although it arose in the context of algebraic geometry and deals with the configuration of curves on an algebraic surface, we have recently observed that…

We explore systems of polynomial equations where we seek complex solutions with absolute value 1. Geometrically, this amounts to understanding intersections of algebraic varieties with tori -- Cartesian powers of the unit circle. We study…

In this note we use the divisorial Zariski decomposition to give a more intrinsic version of the algebraic Morse inequalities.

This thesis studies arithmetic of linear algebraic groups. It involves studying the properties of linear algebraic groups defined over global fields, local fields and finite fields, or more generally the study of the linear algebraic groups…

We prove two theorems on the locally finite decompositions of the cones of divisors by the cones which correspond to canonical and minimal models. We introduce the concept of the numerical linear systems in order to simplify the argument on…

In this paper, we collect some fundamental properties of the arithmetic restricted volumes (or the arithmetic multiplicities) of the adelically metrized line bundles. The arithmetic restricted volume has the concavity property and…

We construct a Zariski decomposition for cycle classes of arbitrary codimension. This decomposition is an analogue of well-known constructions for divisors. Examples illustrate how Zariski decompositions of cycle classes reflect the…

We prove that the base space of a log smooth family of log canonical pairs of log general type is of log general type as well as algebraically degenerate, when the family admits a relative good minimal model over a Zariski open subset of…

We study the maximum likelihood degree of linear concentration models in algebraic statistics. We relate the geometry of the reciprocal variety to that of semidefinite programming. We show that the Zariski closure in the Grassmanian of the…