相关论文: Cubic Surfaces and Borcherds Products
We examine the space of surfaces in $\RR^{3}$ which are complete, properly embedded and have nonzero constant mean curvature. These surfaces are noncompact provided we exclude the case of the round sphere. We prove that the space $\Mk$ of…
We introduce a compact moduli of noncommutative quadrics, and show that it is the weighted projective space of weight (2,4,4,6). We also introduce a compact moduli of potentials for the conifold quiver, and show that it is the weighted…
The Eckardt hypersurface in $\mathbb{P}^{19}$ parameterizes smooth cubic surfaces with an Eckardt point, which is a point common to three of the $27$ lines on a smooth cubic surface. We describe the cubic surfaces lying on the singular…
We show that the irreducible components of any moduli space of semistable representations of a special biserial algebra are always isomorphic to products of projective spaces of various dimensions. This is done by showing that irreducible…
We construct and study the moduli of hypersurfaces in toric orbifolds. Let $X$ be a projective toric orbifold and $\alpha \in Cl(X)$ an ample class. The moduli space is constructed as a quotient of the linear system $|\alpha|$ by $G =…
In this paper we construct a moduli space for marked rational elliptic surfaces of index two as a non-complete toric variety of dimension nine. We also construct compactifications of this moduli space, which are obtained as quotients of…
We revisit the work of Lehn-Lehn-Sorger-van Straten on twisted cubic curves in a cubic fourfold not containing a plane in terms of moduli spaces. We show that the blow-up $Z'$ along the cubic of the irreducible holomorphic symplectic…
We study the moduli spaces of flat surfaces with prescribed conical singularities. Veech showed that these spaces are diffeomorphic to the moduli spaces of marked Riemann surfaces, and endowed with a natural volume form depending on the…
In this article we study the deformation theory of conically singular Cayley submanifolds. In particular, we prove a result on the expected dimension of a moduli space of Cayley deformations of a conically singular Cayley submanifold.…
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…
We consider the local deformation problem of coisotropic submanifolds inside Poisson manifolds. To this end the groupoid of coisotropic sections (with respect to some tubular neighbourhood) is introduced. Although the geometric content of…
We find explicit projective models of a compact Shimura curve and of a (non-compact) surface which are the moduli spaces of principally polarised abelian fourfolds with an automorphism of order five. The surface has a 24-nodal canonical…
This article studies moduli spaces of Bridgeland semistable objects in the Kuznetsov component of a cubic fourfold that don't admit a symplectic resolution, i.e., moduli spaces of objects with non-primitve Mukai vector v=mv_0 that is not of…
We determine explicit birational models over Q for the modular surfaces parametrising pairs of N-congruent elliptic curves in all cases where this surface is an elliptic surface. In each case we also determine the rank of the Mordell-Weil…
Some ball-quotient orbifolds are related by covering maps. We exploit these coverings to find infinite towers of orbifolds uniformized by the complex 2-ball and some orbifolds over K3 surfaces uniformized by the 2-ball. Corresponding…
We analyse the moduli space and the structure of noncommutative 3-spheres. We develop the notion of central quadratic form for quadratic algebras, and prove a general algebraic result which considerably refines the classical homomorphism…
In this paper, we develop a new method to classify abelian automorphism groups of hypersurfaces. We use this method to classify (Theorem 4.2) abelian groups that admit a liftable action on a smooth cubic fourfold. A parallel result (Theorem…
We consider the moduli space of genus 4 curves endowed with a $g^1_3$ (which maps with degree 2 onto the moduli space of genus 4 curves). We prove that it defines a degree $\frac{1}{2}(3^{10}-1)$ cover of the 9-dimensional Deligne-Mostow…
We define a class of surfaces corresponding to the ADE root lattices and construct compactifications of their moduli spaces as quotients of projective varieties for Coxeter fans, generalizing Losev-Manin spaces of curves. We exhibit modular…
In this paper we first show that on projective manifolds (M, {\omega}), there are holomorphic determinant bundles (in the sense of Knusden-Mumford used by Bismut, Gillet, Soule) which play the role of the geometric quantum bundle, namely…