Related papers: Support theorem of universal compactified Jacobian…

We prove the universal lifting theorem: for an $\alpha$-simply connected and $\alpha$-connected Lie groupoid $\gm$ with Lie algebroid $A$, the graded Lie algebra of multi-differentials on $A$ is isomorphic to that of multiplicative…

We prove that the moduli space of complete Riemannian metrics of bounded geometry and uniformly positive scalar curvature on an orientable 3-manifold is path-connected. This generalizes the main result of the fourth author [Mar12] in the…

A generalization of the Hartogs theorem is proved for a class of Tubes structures. We assume that the intervening commutative Lie algebra admits at least a number of globally solvable generators greater or equal to the structure…

We prove that any commutative group scheme over an arbitrary base scheme of finite type over a field with connected fibers and admitting a relatively ample line bundle is polarizable in the sense of Ng\^o. This extends the applicability of…

We will prove a decomposition for Wasserstein geodesics in the following sense: let $(X,d,m)$ be a non-branching metric measure space verifying $\mathsf{CD}_{loc}(K,N)$ or equivalently $\mathsf{CD}^{*}(K,N)$. We prove that every geodesic…

Let Q be a finite quiver without oriented cycles. Denote by U --> M the fine moduli space of stable thin sincere representations of Q with respect to the canonical stability notion. We prove Ext^i(U,U) = 0 for all i >0 and compute the…

For each compact almost Kahler manifold $(X,\om,J)$ and an element A of $H_2(X;Z)$, we describe a closed subspace $\ov{\frak M}_{1,k}^0(X,A;J)$ of the moduli space $\ov{\frak M}_{1,k}(X,A;J)$ of stable J-holomorphic genus-one maps such that…

We show that if $u$ is a compactly supported distribution on the complex plane such that, for every pair of entire functions $f,g$, \[ \langle u,f\overline{g}\rangle=\langle u,f\rangle\langle u,\overline{g}\rangle, \] then $u$ is supported…

We define a certain compactifiction of the general linear group and give a modular description for its points with values in arbitrary schemes. This is a first step in the construction of a higher rank generalization of Gieseker's…

The cherry on top of this stacky paper is the following: for any g>1 we give a finite group G such that the moduli space of connected admissible G-covers of genus g is a smooth, fine moduli space, which is a Galois cover of the moduli space…

The long-standing problem of the perfectness of the compactly supported equivariant homeomorphism group on a $G$-manifold (with one orbit type) is solved in the affirmative. The proof is based on an argument different than that for the case…

In the significant work of [2], Alinhac proved the global existence of small solutions for 2D quasilinear wave equations under the null conditions. The proof heavily relies on the fact that the initial data have compact support [22].…

We prove a general factorization theorem for maps with hereditarily indecomposable fibers and apply it to reprove a theorem of Mackoviak on the existence of universal hereditarily indecomposable continua.

For a natural class of cohomology theories with support (including \'etale or pro-\'etale cohomology with suitable coefficients), we prove a moving lemma for cohomology classes with support on smooth quasi-projective k-varieties that admit…

Let $k$ be a field of characteristic $p>0$, and let $W$ be a complete discrete valuation ring of characteristic $0$ that has $k$ as its residue field. Suppose $G$ is a finite group and $G^{\mathrm{ab},p}$ is its maximal abelian $p$-quotient…

Let $kG$ be the group algebra of a finite group scheme defined over a field $k$ of characteristic $p>0$. Associated to any closed subset $V$ of the projectivized prime ideal spectrum $\operatorname{Proj} \operatorname{H}^*(G,k)$ is a thick…

In a previous paper, the first two named authors established an isomorphism between the moduli space of framed flags of sheaves on the projective plane and the moduli space of stable representations of a certain quiver. In the present note,…

Let $X$ be a compact Riemann surface of genus $g \geq 3$ and $S$ a finite subset of $X$. Let $\xi$ be fixed a holomorphic line bundle over $X$ of degree $d$. Let $\mathcal{M}_{pc}(r, d, \alpha)$ (respectively, $\mathcal{M}_{pc}(r, \alpha,…

The focus of our paper is on the complex Grassmann manifolds $G_{n,2}$ which appear as one of the fundamental objects in developing the interaction between algebraic geometry and algebraic topology. In his well-known paper Kapranov has…

The stable reduction theorem of Deligne and Mumford --- The moduli space of smooth projective curves of genus $g$ is a quasi-projective algebraic variety, but is not projective. To understand its geometry, it may be crucial to consider…