Related papers: Higher-dimensional analogues of stable curves

We study the spaces of stable real and quaternionic vector bundles on a real algebraic curve. The basic relationship is established with unitary representations of an extension Z/2 by the fundamental group. By comparison with the space of…

We prove that the moduli space of stable maps of degree 2 to the moduli space of rank 2 stable bundles of fixed determinant O(-x) over a smooth projective curve of genus g>2 has two irre- ducible components which intersect transversely. One…

We construct the Mumford-Knudsen space of n pointed stable rational curves by a sequence of explicit blow-ups from the GIT quotient (P^1)^n//SL(2) with respect to the symmetric linearization O(1,...,1). The intermediate blown-up spaces turn…

Let $X = S \times E$ be the product of a K3 surface $S$ and an elliptic curve $E$. Reduced stable pair invariants of $X$ can be defined via (1) cutting down the reduced virtual class with incidence conditions or (2) the Behrend function…

The moduli space of stable relative maps to the projective line combines features of stable maps and admissible covers. We prove all standard Gromov-Witten classes on these moduli spaces of stable relative maps have tautological…

We provide a construction of the moduli spaces of framed Hitchin pairs and their master spaces. These objects have come to interest as algebraic versions of solutions of certain coupled vortex equations by work of Lin and Stupariu. Our…

We study compact stable embedded minimal surfaces whose boundary is given by two collections of closed smooth Jordan curves in close planes of Euclidean 3-space. Our main result is a classification of these minimal surfaces, under certain…

We give a method to construct stable vector bundles whose rank divides the degree over curves of genus bigger than one. The method complements the one given by Newstead. Finally, we make some systematic remarks and observations in…

We construct stable vector bundles on the space of symmetric forms of degree d in n+1 variables which are equivariant for the action of SL_{n+1}(C), and admit an equivariant free resolution of length 2. For n=1, we obtain new examples of…

Let X be a smooth projective curve of genus g \geq 2 over an algebraically closed field k of characteristic p > 0. Let M_X be the moduli space of semistable rank-2 vector bundles over X with trivial determinant. The relative Frobenius map…

The genus of projective curves discretely separates decidedly different two variable algebraic relations. So, we can focus on the connected moduli M_g of genus g curves. Yet, modern applications require a data variable (function) on such…

Let X and Y be smooth varieties of dimensions n-1 and n over an arbitrary algebraically closed field, f:X-> Y a finite map that is birational onto its image. Suppose that f is curvilinear; that is, at every point of X, the Jacobian has rank…

We construct modular compactifications of the universal Jacobian stack over the moduli stack of reduced curves with marked points depending on stability parameters obtained out of fixing a vector bundle on the universal curve. When…

Let $(X,c_X)$ be a convex projective surface equipped with a real structure. The space of stable maps $\bar{\mathcal{M}}_{0,k}(X,d)$ carries different real structures induced by $c_X$ and any order two element $\tau$ of permutation group…

We construct an infinite collection of universal -- independent of $(g,n)$ -- polynomials in the Miller-Morita-Mumford classes $\kappa_m\in H^{2m}( \overline{\cal M}_{g,n},\bq)$, defined over the moduli space of genus $g$ stable curves with…

For $L \hookrightarrow X$ a Lagrangian embedding associated with a real homogeneous space, we construct the moduli space of stable holomorphic discs mapping to $(X,L)$ as an orbifold with corners equipped with a group action. Some essential…

We investigate the minimal singularities of metrics on a big line bundle $L$ over a projective manifold when the stable base locus $Y$ of $L$ is a submanifold of codimension $r\geq 1$. Under some assumptions on the normal bundle and a…

We construct master spaces for oriented torsion free sheaves coupled with morphisms into a fixed reference sheaf. These spaces are projective varieties endowed with a natural $\C^*$-action. The fixed point set of this action contains the…

Simple polyhedra are $2$-dimensional polyhedra and important objects in low-dimensional geometry and in the applications of {\it fold} maps, defined as smooth maps regarded as higher dimensional variants of Morse functions. For example,…

We present the program Boundary, whose source files are available at http://people.sissa.it/~maggiolo/boundary/. Given two natural numbers g and n satisfying 2g+n-2>0, the program generates all genus g stable graphs with n unordered marked…