Related papers: New nef divisors on $\bar{M}_{0,n}$

We establish a new moduli theory for divisors, that interpolates between the Hilbert scheme and the Cayley-Chow variety. This completes the last step in the construction of a good moduli theory for stable pairs $(X,\Delta)$.

We introduce and study the GIT CONE of $\bar{M}_{0,n}$, which is generated by the pullbacks of the natural ample line bundles on the GIT quotients $(\mathbb P^1)^n//SL(2)$. We give an explicit formula for these line bundles and prove a…

In this paper we study those submonoids of $\mathbb{N}^d$ which a non-trivial pseudo-Frobenius set. In the affine case, we prove that they are the affine semigroups whose associated algebra over a field has maximal projective dimension…

We prove that on a Bott-Samelson variety $X$ every movable divisor is nef. This enables us to consider Zariski decompositions of effective divisors, which in turn yields a description of the Mori chamber decomposition of the effective cone.…

Let $f:X\to S$ be a projective morphism of normal varieties. Assume $U$ is an open subset of $S$ and $L_U$ is a $\mathbb{Q}$-divisor on $X_U:=X\times_S U$ such that $L_U\equiv_U 0$. We explore when it is possible to extend $L_U$ to a global…

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…

In this note I extend two theorems of Sommese regarding abelian varieties to arbitrary characteristic; that an abelian variety cannot be an ample divisor in a smooth projective variety and that a cone over an abelian variety of dimension at…

We consider polynomials of the form t^n-1 and determine when members of this family have a divisor of every degree in Z[t]. With F(x) defined to be the number of such integers up to x, we prove the existence of two positive constants c_1…

We introduce a new technique for proving positivity of certain divisor classes on $\bar{M}_{0,n}$ and its weighted variants. Our methods give an unconditional description of the spaces of symmetric weighted pointed rational curves as log…

We propose a linear version of the weighted bounded negativity conjecture. It considers a smooth projective surface $X$ over an algebraically closed field of characteristic zero and predicts the existence of a common lower bound on…

Let $H$ be an ample line bundle on a non-singular projective surface $X$, and $M(H)$ the coarse moduli scheme of rank-two $H$-semistable sheaves with fixed Chern classes on $X$. We show that if $H$ changes and passes through walls to get…

T.Kishimoto raised the problem to classify all compactifications of contractible affine 3-folds into smooth Fano 3-folds with second Betti number two and classified such compactifications whose log canonical divisors are not nef. In this…

In this short note we will show that every homogeneous strictly nef vector bundle on a complex flag variety is ample. Following this, we consider whether ampleness of a bundle on an abelian variety can be tested on curves.

We give a general formula for generators of the NL-cone, the cone of effective linear combinations of irreducible components of Noether-Lefschetz divisors, on an orthogonal modular variety. We then fully describe the NL-cone and its…

The paper is devoted to highlighting several novel aspects of the moduli space of curves of genus 13, the first genus g where phenomena related to K3 surfaces no longer govern the birational geometry of M_g. We compute the class of the…

This paper deals with the Nash problem, which claims that there are as many families of arcs on a singular germ of surface $U$ as there are essential components of the exceptional divisor in the desingularisation of this singularity. Let…

This is a large audience version of our previous work (see math.AG/0301146) in which we prove the existence of an (exact) equivalence between the category of coherent analytic sheaves and the category of $\bar{\partial}$-coherent sheaves.…

We compute many new classes of effective divisors in $\overline{\mathcal{M}}_{g,n}$ coming from the strata of abelian differentials and efficiently reproduce many known results obtained by alternate methods. Our method utilises maps between…

We describe nef vector bundles on a projective space with first Chern class three and second Chern class eight over an algebraically closed field of characteristic zero by giving them a minimal resolution in terms of a full strong…

We prove lower bounds for the minimum distance of algebraic geometry codes over surfaces whose canonical divisor is either nef or anti-strictly nef and over surfaces without irreducible curves of small genus. We sharpen these lower bounds…