Related papers: A support theorem for nested Hilbert schemes of pl…

In this paper we define the notion of slow divergence integral along sliding segments in regularized planar piecewise smooth systems. The boundary of such segments may contain diverse tangency points. We show that the slow divergence…

We show that a particular subfunctor of the relative logarithmic Picard functor for families of aligned, log semistable curves over a regular base scheme and smooth over an open dense subscheme of the base is representable by a smooth…

The Hilbert scheme of points $\mathrm{Hilb}^n(S)$ of a smooth surface $S$ is a well-studied parameter space, lying at the interface of algebraic geometry, commutative algebra, representation theory, combinatorics, and mathematical physics.…

This paper introduces the notion of a derived splinter. Roughly speaking, a scheme is a derived splinter if it splits off from the coherent cohomology of any proper cover. Over a field of characteristic 0, this condition characterises…

In its simplest form the Decomposition Theorem asserts that the rational intersection cohomology of a complex projective variety occurs as a summand of the cohomology of any resolution. This deep theorem has found important applications in…

These are classified by the direction of approximation (from above or below), the set family types (partition or covering) of simple functions, the coefficient signature (non-negative or signed), and cardinal number of terms of simple…

We investigate the behavior of semi-orthogonal decompositions of bounded derived categories of singular varieties under flat deformations to smooth varieties. We consider a Q-Gorenstein smoothing of a surface with a quotient singularity,…

We study multivariate trigonometric polynomials, satisfying a set of constraints close to the known Strung-Fix conditions. Based on the polyphase representation of these polynomials relative to a general dilation matrix, we develop a simple…

For a subvariety of a smooth projective variety, consider the family of smooth hypersurfaces of sufficiently large degree containing it, and take the quotient of the middle cohomology of the hypersurfaces by the cohomology of the ambient…

We develop a version of Hodge theory for a large class of smooth formally proper quotient stacks $X/G$ analogous to Hodge theory for smooth projective schemes. We show that the noncommutative Hodge-de Rham sequence for the category of…

Let $S$ be a smooth projective surface over $\mathbb{C}$. We study the local and global geometry of the nested Hilbert scheme of points $S^{[n,n+1,n+2]}$. In particular, we show that $S^{[n,n+1,n+2]}$ is an irreducible local complete…

We generalize some results in the literature on movable curve classes and slope stability of coherent sheaves on smooth projective varieties to the case of smooth proper DM stacks admitting projective coarse moduli spaces. As an…

We use the Springer correspondence to give a partial characterization of the irreducible representations which appear in the Tymoczko dot-action of the Weyl group on the cohomology ring of a regular semisimple Hessenberg variety. In type A,…

We define Strebel differentials for stable complex curves, prove the existence and uniqueness theorem that generalizes Strebel's theorem for smooth curves, prove that Strebel differentials form a continuous family over the moduli space of…

Smooth complex surfaces polarized with an ample and globally generated line bundle of degree three and four, such that the adjoint bundle is not globally generated, are considered. Scrolls of a vector bundle over a smooth curve are shown to…

In this article, we give a proof for a geometric presentation theorem for any irreducible scheme $X$ smooth projective over a discrete valuation ring $R$. As a consequence, for any reductive $R$-group scheme $\mathbf{G}$, we prove that any…

In this paper we state and prove a higher index theorem for an odd-dimensional connected spin riemannian manifold $(M,g)$ which is partitioned by an oriented closed hypersurface $N$. This index theorem generalizes a theorem due to N. Higson…

Let $f \colon X \to Y$ be the blow-up of a smooth projective variety $Y$ along its codimension two smooth closed subvariety. In this paper, we show that the moduli space of stable sheaves on $X$ and $Y$ are connected by a sequence of…

We investigate the Hilbert scheme of points on curves with n-fold singularities, that is curves that look locally around their singular points as the axis in an affine space. We describe the structure and number of its irreducible…

Let $k$ be an algebraically closed field and let $A$ be a finitely generated $k-$algebra. We show that the scheme of n-dimensional representations of $A$ is smooth when $A$ is hereditary and coherent. We deduce from this the smoothness of…