Related papers: On nef subvarieties

On a projective surface it is well-known that the set of curves orthogonal to a nef line bundle is either finite or uncountable. We show that this dichotomy fails in higher dimension by constructing a nef line bundle on a threefold which is…

We show that local complete intersection subvarieties of smooth projective varieties, which have partially ample normal bundle, possess the G2-property. This generalizes results of Hartshorne and B\u{a}descu-Schneider.

In this article, we investigate Serrano's conjecture for strictly nef divisors on projective bundles over higher dimensional smooth projective varieties.

In this article we prove new results on projective normality and normal presentation of adjunction bundle associated to an ample and globally generated line bundle on higher dimensional smooth projective varieties with nef canonical bundle.…

In this paper we show some Lefschetz-type theorems for the effective cone of Hyperk\"ahler varieties. In particular we are able to show that the inclusion of any smooth ample divisor induces an isomorphism of effective cones. Moreover we…

We apply the theory of the Chow-Mumford line bundle as developed by Arezzo-et-al and build on earlier key insights of Paul and Tian (see \cite{Arezzo:DellaVedova:LaNave} and the references therein). In particular, we give an explicit…

We study the nef cone of self-products of a curve. When the curve is very general of genus $g>2$, we construct a nontrivial class of self-intersection 0 on the boundary of the nef cone. Up to symmetry, this is the only known nontrivial…

The present paper concerns the invariants of generically nef vector bundles on ruled surfaces. By Mehta - Ramanathan Restriction Theorem and by Miyaoka characterization of semistable vector bundles on a curve, the generic nefness can be…

By using classical invariant theory, we reduce the $S_{n}$-invariant F-conjecture to a feasibility problem in polyhedral geometry. We show by computer that for $n \le 19$, every integral $S_{n}$-invariant F-nef divisor on the moduli space…

In this paper, we prove the ampleness conjecture and Serrano's conjecture for strictly nef divisors on K-trivial fourfolds. Specifically, we show that any strictly nef divisors on projective fourfolds with trivial canonical bundle and…

The cotangent bundle of a non-uniruled projective manifold is generically nef, due to a theorem of Miyaoka. We show that the cotangent bundle is actually generically ample, if the manifold is of general type and study in detail the case of…

Using currents with minimal singularities, we construct pointwise minimal multiplicities for a real pseudo-effective $(1,1)$-class $\alpha$ on a compact complex $n$-fold $X$, which are the local obstructions to the numerical effectivity of…

We introduce a notion of volume of a normal isolated singularity that generalizes Wahl's characteristic number of surface singularities to arbitrary dimensions. We prove a basic monotonicity property of this volume under finite morphisms.…

Serrrano's Conjecture says that if $L$ is a strictly nef line bundle on a smooth projective variety $X$, then $K_X+tL$ is ample for $ t > dim X+1$. In this paper I will prove a few cases of this conjecture. I will also prove a generalized…

We give a sharp lower bound for the selfintersection of a nef line bundle $L$ on an irregular variety $X$ in terms of its continuous global sections and the Albanese dimension of $X$, which we call the Generalized Clifford-Severi…

In a recent preprint, H. Tsuji gave a number of interesting assertions on the structure of pseudo-effective line bundles on projective manifolds. In particular, he postulated the existence of an almost-holomorphic "reduction map", whose…

Let $C$ be a smooth projective curve over $\mathbb C$. Let $n,d\geq 1$. Let $\mathcal Q$ be the Quot scheme parameterizing torsion quotients of the vector bundle $\mathcal O^n_C$ of degree $d$. In this article we study the nef cone of…

In this paper we show that a smooth toric variety $X$ of Picard number $r\leq 3$ always admits a nef primitive collection supported on a hyperplane admitting non-trivial intersection with the cone $\Nef(X)$ of numerically effective divisors…

We prove that a holomorphic line bundle on a projective manifold is pseudo-effective if and only if its degree on any member of a covering family of curves is non-negative. This is a consequence of a duality statement between the cone of…

In this paper we study the ample cone of the moduli space $\mgn$ of stable $n$-pointed curves of genus $g$. Our motivating conjecture is that a divisor on $\mgn$ is ample iff it has positive intersection with all 1-dimensional strata (the…