Related papers: (Bi-)Cohen-Macaulay simplicial complexes and their…

In this short note, we consider a fiberation f: (X, Delta) to Y between two compact Kahler manifolds with generic fiber of f being a smooth log canonical pair with ample canonical divisor, we prove that the current induced by variation of…

We study the degeneration problem for maximal Cohen-Macaulay modules and give several examples of such degenerations. It is proved that such degenerations over an even-dimensional simple hypersurface singularity of type $(A_n)$ are given by…

We propose the notion of perverse coherent sheaves for symplectic singularities and study its properties. In particular, it gives a basis of simple objects in the Grothendieck group of Poisson sheaves. We show that perverse coherent bases…

Let G be a finite group of automorphisms of a nonsingular complex threefold M such that the canonical bundle omega_M is locally trivial as a G-sheaf. We prove that the Hilbert scheme Y=GHilb M parametrising G-clusters in M is a crepant…

It is proved that the category of simplicial complete bornological spaces over $\mathbb R$ carries a combinatorial monoidal model structure satisfying the monoid axiom. For any commutative monoid in this category the category of modules is…

We examine virtual resolutions of Stanley-Reisner ideals for a product of projective spaces. In particular, we provide sufficient conditions for a simplicial complex to be virtually Cohen-Macaulay (to have a virtual resolution with length…

Let $\A$ be a ring with local units, $\E$ a set of local units for $\A$, $\G$ an abelian group and $\alpha$ a partial action of $\G$ by ideals of $\A$ that contain local units and such that the partial skew group ring $\A\star_{\alpha} \G$…

We study the stable hom relation for Cohen-Macaulay modules over Gorenstein local algebras. We give the sufficient condition to make the stable hom relation a partial order when the base algebra is of finite representation type. As an…

We give a new proof that the opposite of Joyal's disk category $\mathcal{D}_n$ is Berger's wreath product category $\Theta_n = \Delta\wr\cdots\wr\Delta$. Our techniques continue to apply when the simplex category $\Delta$ is replaced by…

A primitive multiple scheme is a Cohen-Macaulay scheme $Y$ such that the associated reduced scheme $X=Y_{red}$ is smooth, irreducible, and that $Y$ can be locally embedded in a smooth variety of dimension $\dim(X)+1$. If $I_X$ is the ideal…

Let A be an integer (d x n) matrix, and assume that the convex hull conv(A) of its columns is a simplex of dimension d-1. Write \NA for the semigroup generated by the columns of A. It was proved by M. Saito [math.AG/0012257] that the…

Let $V$ be a simple vertex operator algebra containing a rank $n$ Heisenberg vertex algebra $H$ and let $C=\text{Com}\left( {H}, {V}\right)$ be the coset of ${H}$ in ${V}$. Assuming that the representation categories of interest are vertex…

We describe new autoequivalences of derived categories of coherent sheaves arising from what we call $\mathbb P^n$-objects of the category. Standard examples arise from holomorphic symplectic manifolds. Under mirror symmetry these…

Let T be a compact complex torus, dim T>2. We show that the category of coherent sheaves on T is independent of the choice of the complex structure, if this complex structure is generic. The proof is independent of math.AG/0205210, where…

Given a finite locally free resolution of a coherent analytic sheaf $\mathcal F$, equipped with Hermitian metrics and connections, we construct an explicit current, obtained as the limit of certain smooth Chern forms of $\mathcal F$, that…

Let X be an algebraic variety with an action of an algebraic group G. Suppose X has a full exceptional collection of sheaves, and these sheaves are invariant under the action of the group. We construct a semiorthogonal decomposition of…

Let $K$ be a field, $B$ a simplicial affine semigroup, and $C(B)$ the corresponding cone. We will present a decomposition of $K[B]$ into a direct sum of certain monomial ideals, which generalizes a construction by Hoa and St\"uckrad. We…

We show that for a vertex decomposable simplicial complex $\Delta$, the Rees algebra of $I_{\Delta^{\vee}}$ is a normal Cohen-Macaulay domain. As consequences, we show that any squarefree weakly polymatroidal ideal is normal and we obtain…

A concrete description of all graded maximal Cohen-Macaulay modules of rank one and two over the affine cone of the simple node (a non-isolated singularity) is given. For this purpose we construct an alghoritm that provides extensions of…

We prove a theorem on how a conclusion on homological dimension of a family of coherent sheaves over a scheme can be done from homological dimension of the restriction of this family to the reduction of the base.