相关论文: On a series of Gorenstein cyclic quotient singular…
We prove a numerical characterization of $\mathbb{P}^n$ for varieties with at worst isolated local complete intersection quotient singularities. In dimension three, we prove such a numerical characterization of $\mathbb{P}^3$ for normal…
We construct a consistent dimer model having the same symmetry as its characteristic polygon. This produces examples of non-commutative crepant resolutions of non-toric non-quotient Gorenstein singularities in dimension 3.
Categorical resolutions of singularities are a replacement of resolution of singularities within the realm of triangulated categories. They allow the study of the derived category of a singular variety $X$ via a triangulated category that…
We study properties of the Hirzebruch class of quotient singularities $\mathbb{C}^n/G$, where $G$ is a finite matrix group. The main result states that the Hirzebruch class coincides with the Molien series of $G$ under suitable substitution…
In this paper we consider Gorenstein stable surfaces with $K^2_X=1$ and positive geometric genus. Extending classical results, we show that such surfaces admit a simple description as weighted complete intersection. We exhibit a wealth of…
We investigate combinatorial aspects of exceptional sequences in the derived category of coherent sheaves on certain smooth and complete algebraic surfaces. We show that to any such sequence there is canonically associated a complete toric…
We consider the quotient group $T(G)$ of the multiple holomorph by the holomorph of a finite $p$-group $G$ of class two for an odd prime $p$. By work of the first-named author, we know that $T(G)$ contains a cyclic subgroup of order…
We construct new complete cotorsion pairs in the categories of modules and chain complexes over a Gorenstein ring $R$, from the notions of Gorenstein homological dimensions, in order to obtain new Abelian model structures on both…
Firstly, we see that the bases of the miniversal deformations of isolated $\mathbb{Q}$-Gorenstein toric singularities are quite restricted. In particular, we classify the analytic germs of embedding dimension $\leq 2$ which are the bases of…
In the classical case of irreducible smooth algebraic curves every genus $2$ curve is hyperelliptic, or in other words there is a complete linear series $g_2^1$ on them. On the other hand if $g > 2$, then a generic smooth curve of genus $2$…
In this paper, we construct a large class of examples of proper, nonprojective crepant resolutions of singularities for Nakajima quiver varieties. These include four and six dimensional examples and examples with $Q$ containing only three…
For an affine, toric Q-Gorenstein variety Y (given by a lattice polytope Q) the vector space T^1 of infinitesimal deformations is related to the complexified vector spaces of rational Minkowski summands of faces of Q. Moreover, assuming Y…
We introduce a certain compactification of the space of projective configurations i.e. orbits of the group $PGL(k)$ on the space of $n$ - tuples of points in $P^{k-1}$ in general position. This compactification differs considerably from…
We consider geometrical problems on Gorenstein hypersurface orbifolds of dimension $n \geq 4$ through the theory of Hilbert scheme of group orbits. For a linear special group $G$ acting on $\CZ^n$, we study the $G$-Hilbert scheme,…
Let $K$ be a compact Lie group with complexification $G$, and let $V$ be a unitary $K$-module. We consider the real symplectic quotient $M_0$ at level $0$ of the homogeneous quadratic moment map as well as the complex symplectic quotient,…
A formula for the dimension of the smoothing component of a $3$-dimensional isolated Cohen--Macaulay singularity is shown. We apply this formula for a $1$-convex threefold with a connected exceptional curve which is blown down to a terminal…
The author has proved that a crepant resolution Y of a Ricci-flat K\"{a}hler cone X admits a complete Ricci-flat K\"{a}hler metric asymptotic to the cone metric in every K\"{a}hler class in H^2_c(Y,\R). These manifolds are generalizations…
We extend the results of Riemannian geometry over finite groups and provide a full classification of all linear connections for the minimal noncommutative differential calculus over a finite cyclic group. We solve the torsion-free and…
Let $(X, L)$ be a polarized Calabi Yau variety (or canonical polarized variety) with crepant singularity. Suppose $\omega_{KE} \in c_1(L)$ (or $\omega_{KE} \in c_1(K_X)$) is the unique Ricci flat current (or Kahler Einstein current with…
We study the following generalization of singularity categories. Let X be a quasi-projective Gorenstein scheme with isolated singularities and A a non-commutative resolution of singularities of X in the sense of Van den Bergh. We introduce…