Related papers: Effective cycles on universal hypersurfaces

Let $X = \mathbb{P}(E_1) \times_C \mathbb{P}(E_2)$ where $C$ is a smooth curve and $E_1$, $E_2$ are vector bundles over $C$.In this paper we compute the pseudo effective cones of higher codimension cycles on $X$.

In this paper we examine the cones of effective cycles on blow ups of projective spaces along smooth rational curves. We determine explicitly the cones of divisors and 1- and 2-dimensional cycles on blow ups of rational normal curves, and…

We compute cones of effective cycles on some blowups of projective spaces in general sets of lines.

Generalizing work done by Miyaoka and others in the case of divisors and of curves, we compute the cones of effective cycles of arbitrary dimension on a projective bundle over a complex projective curve in terms of the numerical data in an…

We study cones of pseudoeffective cycles on the blow up of $({\mathbb P}^1)^n$ at points in very general position, proving some results concerning their structure. In particular we show that in some cases they turn out to be generated by…

In this paper, we study the cones of higher codimension (pseudo)effective cycles on point blow-ups of projective space. We determine bounds on the number of points for which these cones are generated by the classes of linear cycles, and for…

Let $X$ be a cubic hypersurface in $\mathbb P^6$ or a hypersurface of degree greater than equal to $7$ in $\mathbb P^5$. In this note we try to understand, for a very general hyperplane section of $X$, the non-injectivity locus of the…

In this paper and in its sequel [BKLV], we investigate the cone ${\rm Pseff}_n(C_d)$ of pseudoeffective $n$-cycles in the symmetric product $C_d$ of a smooth curve $C$. In the present paper, we study the convex-geometric properties of the…

Let X be a normal projective variety admitting an action of a semisimple group with a unique closed orbit. We construct finitely many rational curves in X, all having a common point, such that every effective one-cycle on X is rationally…

We compute the facets of the effective and movable cones of divisors on the blow-up of $\mathbb{P}^n$ at $n+3$ points in general position. Given any linear system of hypersurfaces of $\mathbb{P}^n$ based at $n+3$ multiple points in general…

We determine five extremal effective rays of the four-dimensional cone of effective surfaces on the toroidal compactification $\overline{\mathcal A}_3$ of the moduli space ${\mathcal A}_3$ of complex principally polarized abelian…

Over any complex cubic hypersurface of dimension at least 2, the Chow group of 1-dimensional cycles is spanned by the lines lying on the hypersurface. The smooth case has already been given several other proofs. -- On montre que sur toute…

Let $\pi: X \to Y$ be a morphism of projective varieties and suppose that $\alpha$ is a pseudo-effective numerical cycle class satisfying $\pi_*\alpha = 0$. A conjecture of Debarre, Jiang, and Voisin predicts that $\alpha$ is a limit of…

We discuss and prove a number of results for calculating characteristic cycles, or graded, enriched characteristic cycles. We concentrate particularly on results related to hypersurfaces.

We study generalizations for higher codimension cycles of several well-known definitions of the nef cone of divisors on a projective variety. These generalizations fix some of the pathologies exhibited by the classical nef cone of higher…

We exhibit infinitely many extremal effective codimension-$k$ cycles in $\overline{\mathcal{M}}_{g,n}$ in the cases $g\geq 3, n\geq g-1$ and $k=2$, $g\geq 2$, $k\leq n-g,g,$ and $g=1$, $k\leq n-2$. Hence in these cases the effective cone is…

We describe the effective and the big cones of a projective symmetric variety. Moreover, we give a necessary and sufficient combinatorial criterion for the bigness of a nef divisor on a projective symmetric variety. When the variety is…

We prove that the maximal number of conics, a priori irreducible of reducible, on a smooth spatial quartic surface is 800, realized by a unique quartic. We also classify quartics with many (at least 720) conics. The maximal number of real…

We show that nef cycle classes on smooth complete spherical varieties are effective, and the products of nef cycle classes are also nef. Let X be a smooth projective spherical variety such that its effective cycle classes of codimension k…

A universal cycle is a compact listing of a class of combinatorial objects. In this paper, we prove the existence of universal cycles of classes of labeled graphs, including simple graphs, trees, graphs with m edges, graphs with loops,…