Related papers: The augmented base locus of real divisors over arb…

We compute the divisor class group of the general hypersurface Y of a complex projective normal variety X of dimension at least four containing a fixed base locus Z. We deduce that completions of normal local complete intersection domains…

This paper shows that on the moduli space of semi-stable vector bundles of fixed rank and determinant (of any degree) on a smooth curve of genus at least two, the base locus of the generalized theta divisor is large provided the rank is…

We approach non-divisorial base loci of big and nef line bundles on irreducible symplectic varieties. While for K3 surfaces, only divisorial base loci can occur, nothing was known about the behaviour of non-divisorial base loci for more…

Since the works of Krasnov and Scheiderer, there has been an interest in studying effective totally real divisors on a curve X defined over a real closed field, i.e., effective divisors supported on the real locus. Scheiderer proved that,…

In this paper, we use canonical bundle formulas to prove some generalizations of an old theorem of Kawamata on the semiampleness of nef and abundant log canonical divisors. In particular, we show that for klt pairs $(X,B)$ with $K_X+B$…

We study the complex-analytic geometry of semi-positive holomorphic line bundles on compact K\"ahler manifolds. In one of our main results, for a $\mathbb{Q}$-effective line bundle satisfying a natural torsion-type assumption, we show the…

Let C be a smooth projective algebraic curve of genus g over the finite field F_q. A classical result of H. Martens states that the Brill-Noether locus of line bundles L in Pic^d C with deg L = d and h^0(L) >= i is of dimension at most…

We prove that the log canonical threshold of the base ideal of a complete linear system on a complex abelian variety is $\ge 1$, and equality holds if and only if the base locus has divisorial components. Consequently the same assertions…

We give the first examples of nef line bundles on smooth projective varieties over finite fields which are not semi-ample. More concretely, we find smooth curves on smooth projective surfaces over finite fields such that the normal bundle…

We propose a subconjecture that implies the semiampleness conjecture for quasi-numerically positive log canonical divisors and prove the semiampleness in some elementary cases.

We prove that the partition rank and the analytic rank of tensors are equal up to a constant, over finite fields of any characteristic and any large enough cardinality depending on the analytic rank. Moreover, we show that a plausible…

Consider a polynomial vector field $\xi$ in $\mathbb{C}^n$ with algebraic coefficients, and $K$ a compact piece of a trajectory. Let $N(K,d)$ denote the maximal number of isolated intersections between $K$ and an algebraic hypersurface of…

Reider's Theorem on the very ampleness of adjoint linear series on a complex projective algebraic surface is extended in two new directions. First, Reider-type inequalities are shown to imply nefness of linear series of the form dH - E on…

The aim of this work is to lay the foundations of differential geometry and Lie theory over the general class of topological base fields and -rings for which a differential calculus has been developed in recent work (collaboration with H.…

Given a Nori motivic local system over a smooth, connected complex algebraic variety, we define its exceptional locus as a way to measure the variation in the motivic complexity of its stalks. The definition is given explicitly in terms of…

We extend Reider's freeness criterion to normal surfaces of characteristic 0. Let Y be a normal surface. Let D be a nef divisor on Y such that K_Y+D is a Cartier divisor. Let x be a point on Y. If x is a base point of |K_Y+D| and…

In this paper we study smooth projective rational surfaces, defined over an algebraically closed field of any characteristic, with pseudo-effective anticanonical divisor. We provide a necessary and sufficient condition in order for any nef…

Boucksom, Favre and Jonsson establish in [4] an analog of Diskant's inequality in convex geometry for nef and big line bundles on a complete algebraic variety over an algebraically closed field of characteristic zero (Theorem F [4]), from…

Recently, the first two authors proved the Alon-Jaeger-Tarsi conjecture on non-vanishing linear maps, for large primes. We extend their ideas to address several other related conjectures. We prove the weak Additive Basis conjecture proposed…

The main object of the present paper is a numerical criterion determining when a Weil divisor of a $\Q$--factorial complete toric variety admits a positive multiple Cartier divisor which is either numerically effective (nef) or ample. It is…