Related papers: Explicit stable models of elliptic surfaces with s…

The purpose of this article is to give an interpretation of real projective structures and associated cohomology classes in terms of connections, sections, etc. satisfying elliptic partial differential equations in the spirit of Hodge…

We classify and expose all the gradient Ricci solitons on complete surfaces, open or closed, with curvature bounded below, and possibly with a discrete set of cone-like singular points that arise naturally. We give a precise qualitative…

We introduce a compact moduli scheme of marked noncommutative cubic surfaces as the GIT moduli scheme of relations of a quiver associated with a full strong exceptional collection on a cubic surface. It is a toric variety containing the…

Following ideas of Lurie, we give in this article a general construction of equivariant elliptic cohomology without restriction to characteristic zero. Specializing to the universal elliptic curve we obtain in particular equivariant spectra…

We introduce in this article a new method to estimate the minimum distance of codes from algebraic surfaces. This lower bound is generic, i.e. can be applied to any surface, and turns out to be ``liftable'' under finite morphisms, paving…

Positive solutions of homogeneous Dirichlet boundary value problems or initial-value problems for certain elliptic or parabolic equations must be radially symmetric and monotone in the radial direction if just one of their level surfaces is…

We study the non-emptyness of moduli of stable sheaves on an elliptic ruled surface with a nef. anticanonical bundle.

Bielliptic surfaces are the last family of Kodaira dimension zero algebraic surfaces without a classification result for the Chern characters of stable sheaves. We rectify this and prove such a classification using a combination of…

In this paper we propose an elementary topological approach which unifies and extends various different results concerning fixed points and periodic points for maps defined on sets homeomorphic to rectangles embedded in euclidean spaces. We…

We use a graph to define a new stability condition for algebraic moduli spaces of rational curves. We characterize when the tropical compactification of the moduli space agrees with the theory of geometric tropicalization. The…

We consider area preserving maps of surfaces and extend Mather's result on the equality of the closure of the four branches of saddles. He assumed elliptic fixed points to be Moser stable, while we require only that the derivative at this…

The problem addressed here can be concisely formulated as follows: given a stable surface orientation with a known reconstruction and given a direction in the plane of this surface, find the atomic structure of the steps oriented along that…

In this paper, we present a methodology for stability analysis of a general class of systems defined by coupled Partial Differential Equations (PDEs) with spatially dependent coefficients and a general class of boundary conditions. This…

Piecewise smooth maps are known to exhibit a wide range of dynamical features including numerous types of periodic orbits. Predicting regions in parameter space where such periodic orbits might occur and determining their stability is…

We study stability conditions on reducible Kodaira curves obtained from degenerations of elliptic curves. We describe connected components of the spaces of stability conditions and compute the groups of deck transformations of those…

We prove rationality results for moduli spaces of elliptic K3 surfaces and elliptic rational surfaces with fixed monodromy groups.

In this paper, we completely work out the log minimal model program for the moduli space of stable curves of genus three. We employ a rational multiple $\alpha\delta$ of the divisor $\delta$ of singular curves as the boundary divisor,…

We prove asymptotic formulas for cyclicity of reductions of elliptic curves over the rationals in a family of curves having specified torsion. These results agree with established conditional results and with average results taken over…

Miranda and Persson classified all extremal rational elliptic surfaces in characteristic zero. We show that each surface in Miranda and Persson's classification has an integral model with good reduction everywhere (except for those of type…

Let C/K: F = 0 be a smooth plane quartic over a complete discrete valuation field K. In a previous paper the authors togetehr with Q. Liu give various characterizations of the reduction (i.e. non-hyperelliptic genus 3 curve, hyperelliptic…