Related papers: Noncommutative quadric surfaces and noncommutative…
We show that the moduli space of all Calabi-Yau manifolds that can be realized as hypersurfaces described by a transverse polynomial in a four dimensional weighted projective space, is connected. This is achieved by exploiting techniques of…
Recall that the moduli space of smooth (that is, stable) cubic curves is isomorphic to the quotient of the upper half plane by the group of fractional linear transformations with integer coefficients. We establish a similar result for…
We study the weight 11 part of the compactly supported cohomology of the moduli space of curves $M_{g,n}$, using graph complex techniques, with particular attention to the case $n = 0$. As applications, we prove new nonvanishing results for…
We study the moduli space of congruence classes of isometric surfaces with the same mean curvature in 4-dimensional space forms. Having the same mean curvature means that there exists a parallel vector bundle isometry between the normal…
We describe recent work on preprojective algebras and moduli spaces of their representations. We give an analogue of Kac's Theorem, characterizing the dimension types of indecomposable coherent sheaves over weighted projective lines in…
This is the third paper in a series of work on weighted stable elliptic surfaces - elliptic fibrations with section and marked fibers weighted between zero and one. Motivated by Hassett's weighted pointed stable curves, we use the log…
We prove that the weight-two Hodge structure of moduli spaces of torsion-free sheaves on a K3 surface is as described by Mukai (the rank is arbitrary but we assume the first Chern class is primitive). We prove the moduli space is an…
We construct a compact nonpositively curved squared 2-complex whose universal cover contains a flat plane that is not the limit of periodic flat planes.
In this paper we show that the homology of a certain natural compactification of the moduli space, introduced by Kontsevich in his study of Witten's conjectures, can be described completely algebraically as the homology of a certain…
We study the weight 2 graded piece of the compactly supported rational cohomology of the moduli spaces of curves $M_{g,n}$ and show that this can be computed as the cohomology of a graph complex that is closely related to graph complexes…
A non associative, noncommutative algebra is defined that may be interpreted as a set of vector modules over a noncommutative surface of rotation. Two of these vector modules are identified with the analogues of the tangent and cotangent…
We study the moduli space of stable sheaves of Euler characteristic 1 supported on curves of bidegree (3, 3) contained in a smooth quadric surface. We show that this moduli space is rational. We compute its Betti numbers by studying the…
We introduce and study smooth compactifications of the moduli space of n labeled points with weights in projective space, which have normal crossings boundary and are defined as GIT quotients of the weighted Fulton-MacPherson…
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…
The family of smooth Fano 3-folds with Picard rank 1 and anticanonical volume 4 consists of quartic 3-folds and of double covers of the 3-dimensional quadric branched along an octic surface. They can all be parametrised as complete…
We show that the moduli spaces of stable sheaves on projective schemes admit certain non-commutative structures, which we call quasi NC structures, generalizing Kapranov's NC structures. The completion of our quasi NC structure at a closed…
In this note we classify compact 4-manifolds with harmonic Weyl tensor and nonnegative biorthogonal curvature
We compute the rational cohomology of the moduli space of non-singular non-hyperelliptic complex projective curves of genus 3 with an odd theta characteristic.
Recently de Thanhoffer de V\"olcsey and Van den Bergh classified the Euler forms on a free abelian group of rank 4 having the properties of the Euler form of a smooth projective surface. There are two types of solutions: one corresponding…
We initiate a study of varieties of minimal degree in weighted projective spaces. We call a weighted projective space $\mathbf{P}(w_0,\dots,w_n)$ divisible if $w_i \mid w_{i+1}$ for all $i$. We provide sharp bounds for when a non-degenerate…