Related papers: Vortices and Jacobian varieties

We study the moduli space of a product of stable varieties over the field of complex numbers, as defined via the minimal model program. Our main results are: (a) taking products gives a well-defined morphism from the product of moduli…

The moduli space $\cM_g$ of nonsingular projective curves of genus $g$ is compactified into the moduli $\bcM_g$ of Deligne-Mumford stable curves of genus $g$. We compactify in a similar way the moduli space of abelian varieties by adding…

We consider $N$ point vortices $s_j$ of strengths $\kappa_j$ moving on a closed (compact, boundaryless, orientable) surface $S$ with riemannian metric $g$. As far as we know, only the sphere or surfaces of revolution, the latter…

Two-dimensional conformal field theory is a powerful tool to understand the geometry of surfaces. Here, we study Liouville conformal field theory in the classical (large central charge) limit, where it encodes the geometry of the moduli…

This note is a summary of our work [OO] which provides an explicit and global moduli-theoretic framework for the collapsing of Ricci-flat Kahler metrics and we use it to study especially the K3 surfaces case. For instance, it allows us to…

The main problem addressed in the paper is the Torelli problem for n-dimensional varieties of general type, more specifically for varieties with ample canonical bundle. It asks under which geometrical condition for a variety the period map…

The new compactification of moduli scheme of Gieseker-stable vector bundles with the given Hilbert polynomial on a smooth projective polarized surface (S;H), over the field k = \bar k of zero characteristic, is constructed in previous…

In this paper, we study the algebraic symplectic geometry of the singular moduli spaces of Higgs bundles of degree $0$ and rank $n$ on a compact Riemann surface $X$ of genus $g$. In particular, we prove that such moduli spaces are…

We study the moduli spaces of k U(N) vortices which are realized by the Higgs branch of a U(k) supersymmetric gauge theory. The theory has 4 supercharges and lives on k D1-branes in a N D3- and NS5-brane background. We realize the vortex…

This work discusses modons, or dipolar vortices, propagating along sloping topography. Two different regimes exist which are studied separately using the surface quasi-geostrophic equations. First, when the modon propagates in the opposite…

We continue our study of the geometry of Nieto's quintic threefold, looking at degenerate surfaces that correspond to certain loci and showing how they arise from a toroidal compactification of a suitable moduli space.

We give a canonical description of the formal moduli space of a vector bundle on a variety; as an application, we prove the closedness of certain differential forms on moduli corresponding to the trace form on the endomorphism algebra of…

We bound the codimension of components of the nonabelian Hodge loci in the relative de Rham moduli space over $\shm_{g,n}$ in terms of the rank and level of a complex variation of Hodge structure. If the rank is $r$ and the level is $\ell$,…

Let ${\mathcal M}_{g,n}$ denote the moduli space of smooth, genus $g\geq 1$ curves with $n\geq 0$ marked points. Let ${\mathcal A}_h$ denote the moduli space of $h$-dimensional, principally polarized abelian varieties. Let $g\geq 3$ and…

The intermediate Jacobian map, which associates to a smooth cubic threefold its intermediate Jacobian, does not extend to the GIT compactification of the space of cubic threefolds, not even as a map to the Satake compactification of the…

The moduli space of Riemann surfaces of genus $g\geq 2$ is (up to a finite \'etale cover) a complex manifold and so it makes sense to speak of its Dolbeault cohomological dimension. The conjecturally optimal bound is $g-2$. This expectation…

Motivated by DeVleming's work on moduli of surfaces in $\mathbb{P}^3$ and Chen-Hu-Jiang's work on moduli of threefolds with volume $2$ and geometric genus $4$, we study the deformation of pairs of $\mathbb{P}^3$ and hypersurfaces using the…

We consider the cell decomposition of the moduli space of real genus two curves with a marked point on the only real oval. The cells are enumerated by certain graphs with their weights describing the complex structure on a curve. We show…

Given a compact Riemannian manifold with boundary, we prove that the space of embedded, which may be improper, free boundary minimal hypersurfaces with uniform area and Morse index upper bound is compact in the sense of smoothly graphical…

We discuss the K\"ahler quantization of moduli spaces of vortices in line bundles over compact surfaces $\Sigma$. This furnishes a semiclassical framework for the study of quantum vortex dynamics in the Schr\"odinger-Chern-Simons model. We…