Related papers: Nef Cone of a Generalized Kummer 4-fold

We show that the blow-up of a generalized Kahler 4-manifold in a nondegenerate complex point admits a generalized Kahler metric. As with the blow-up of complex surfaces, this metric may be chosen to coincide with the original outside a…

The Coble cubics were discovered more than a century ago in connection with genus two Riemann surfaces and theta functions. They have attracted renewed interest ever since. Recently, they were reinterpreted in terms of alternating…

We study the geometry of Nieto's quintic threefold (Barth & Nieto, J. Alg. Geom. 3, 1994) and the Kummer and abelian surfaces that correspond to special loci.

Using equivariant geometry, we find a universal formula that computes the number of times a general cubic surface arises in a family. As applications, we show that the PGL(4) orbit closure of a generic cubic surface has degree 96120, and…

This paper gives sharp linear bounds on the genus of a normal surface in a triangulated compact, orientable 3--manifold in terms of the quadrilaterals in its cell decomposition---different bounds arise from varying hypotheses on the surface…

We introduce Koras-Russell fiber bundles over algebraically closed fields of characteristic zero. After a single suspension, this exhibits an infinite family of smooth affine A1-contractible 3-folds. Moreover, we give examples of stably…

We analyze the ample and moving cones of holomorphic symplectic manifolds, in light of recent advances in the minimal model program. As an application, we establish a numerical criterion for ampleness of divisors on fourfolds…

Let k be an algebraically closed field, let K/k be a finitely generated field extension of transcendence degree 2 with automorphism sigma, and let A be an N-graded subalgebra of Q = K[t; sigma] with A_n finite dimensional over k for all n.…

Let X be a smooth projective surface of irregularity 0. The Hilbert scheme of n points on X parameterizes zero-dimensional subschemes of X of length n. In this paper, we discuss general methods for studying the cone of ample divisors on the…

The universal Kummer threefold is a 9-dimensional variety that represents the total space of the 6-dimensional family of Kummer threefolds in 7-dimensional projective space. We compute defining polynomials for three versions of this family,…

This paper relates the boundary term in the Chern-Gauss-Bonnet formula on 4-manifolds M with the renormalized volume V, as defined in the AdS/CFT correspondence, for asymptotically hyperbolic Einstein metrics on M. In addition, we compute…

Let $K$ be a 1-dimensional function field over an algebraically closed field of characteristic $0$, and let $A/K$ be an abelian surface. Under mild assumptions, we prove a Lehmer-type lower bound for points in $A(\bar{K})$. More precisely,…

In this paper we study the general affine differential geometry of surfaces in affine space $A^3$. For a regular elliptical surface we define a moving frame of minimal order and get the complete system of differential invariants. As an…

Given a closed four-manifold $X$ with an indefinite intersection form, we consider smoothly embedded surfaces in $X \setminus $int$(B^4)$, with boundary a knot $K \subset S^3$. We give several methods to bound the genus of such surfaces in…

We discuss some consequences of the existence of the holomorphic quadratic Hopf differential on a conformally immersed constant mean curvature topological disc with analytic boundary. In particular, we derive a formula for the mean…

We find formulas for the birational maps from a Kummer surface K and its dual K^* to their common minimal desingularization S. We show how the nodes of K blow up. Then we give a description of the group of linear automorphisms of S.

The weighted bounded negativity conjecture considers a smooth projective surface $X$ and looks for a common lower bound on the quotients $C^2/(D\cdot C)^2$, where $C$ runs over the integral curves on $X$ and $D$ over the big and nef…

A desmic quartic surface is a birational model of the Kummer surface of the self-product of an elliptic curve. We recall the classical geometry of these surfaces and study their analogs in arbitrary characteristic. Moreover, we discuss the…

We prove a bound relating the volume of a curve near a cusp in a hyperbolic manifold to its multiplicity at the cusp. The proof uses a hybrid technique employing both the geometry of the uniformizing group and the algebraic geometry of the…

We show that the problem of deciding whether a knot in a fixed closed orientable 3-dimensional manifold bounds a surface of genus at most $g$ is in co-NP. This answers a question of Agol, Hass, and Thurston in 2002. Previously, this was…