Related papers: Logarithmic forms and singular projective foliatio…

We consider elliptic fibrations with arbitrary base dimensions, and generalise previous work by the second author. In particular, we check universal closedness for the moduli of semistable objects with respect to a polynomial stability that…

We show stability of the $L^2$-projection onto Lagrange finite element spaces with respect to (weighted) $L^p$ and $W^{1,p}$-norms for any polynomial degree and for any space dimension under suitable conditions on the mesh grading. This…

We identify a class of singular algebraic foliations whose leaves through singular points retain regularity. The proof consists in showing existence of residual gerbes for certain formal stacks, which do not enjoy smooth presentations. As…

In this article, we prove the Sarkisov Program for co-rank one foliations with suitable singularities on normal projective threefolds. We also exibit a weaker version of birational super-rigidity between two foliated Mori fiber spaces with…

Let R be an affine algebra of dimension n \geq 3 over an algebraically closed field k. Suppose char k =0 or char k =p \geq n. Let g,f_1,...,f_r be a R-regular sequence and A=R[f_1/g,...,f_r/g]. Let P be a projective A-module of rank n-1…

For each positive integer $Q\in\mathbb{Z}_{\geq 2}$, we prove a multi-valued $C^{1,\alpha}$ regularity theorem for varifolds in the class $\mathcal{S}_Q$, i.e., stable codimension one stationary integral $n$-varifolds which have no…

In this note, we aim to prove the finite semi-algebraic chamber decomposition theorem for K-semi(poly)stability under the assumption of the log boundedness of K-semistable degenerations. This boundedness assumption is naturally arising from…

We introduce a notion of normal form for transversely projective structures of singular foliations on complex manifolds. Our first main result says that this normal form exists and is unique when ambient space is two-dimensional. From this…

We obtain a fine structural result for two-dimensional mod$(q)$ area-minimizing currents of codimension one, close to flat singularities. Precisely, we show that, locally around any such singularity, the current is a…

We associate to every matroid M a polynomial with integer coefficients, which we call the Kazhdan-Lusztig polynomial of M, in analogy with Kazhdan-Lusztig polynomials in representation theory. We conjecture that the coefficients are always…

We study the rationality properties of the moduli space $\mathcal{A}_g$ of principally polarised abelian $g$-folds over $\mathbb{Q}$ and apply the results to arithmetic questions. In particular we show that any principally polarised abelian…

Let $\Lambda$ be a finite dimensional algebra over an algebraically closed field. We exhibit slices of the representation theory of $\Lambda$ that are always classifiable in stringent geometric terms. Namely, we prove that, for any…

We establish (Theorem 3.6) polynomial-growth estimates for the Fourier coefficients of holomorphic logarithmic vector-valued modular forms.

In this paper, we establish an innovative framework in logarithmic Hodge theory for toroidal varieties, introducing weighted toroidal structures and developing a systematic obstruction theory for Hodge classes. Building upon recent advances…

Let k be a field and q a non-zero element of k. In Part I, we have exhibited a 6-dimensional k-algebra A = A(q) and we have shown that if q has infinite multiplicative order, then A has a 3-dimensional local module which is…

In this article, we study projective log smooth pairs with numerically flat normalized logarithmic tangent bundle. Generalizing works of Jahnke-Radloff and Greb-Kebekus-Peternell, we show that, passing to an appropriate finite cover and up…

Perfect quadratic forms give a toroidal compactification of the moduli space of principally polarized abelian g-folds that is Q-factorial and whose ample classes are characterized, over any base. In characteristic zero it has canonical…

Let $X$ be a compact Riemann surface of genus $g \geq 3$. We consider the moduli space of holomorphic connections over $X$ and the moduli space of logarithmic connections singular over a finite subset of $X$ with fixed residues. We…

We investigate under what conditions holomorphic forms defined on the regular locus of a reduced complex space extend to holomorphic (or logarithmic) forms on a resolution of singularities. We give a simple necessary and sufficient…

We study polynomial and exponential stability for $C_{0}$-semigroups using the recently developed theory of operator-valued $(L^{p},L^{q})$ Fourier multipliers. We characterize polynomial decay of orbits of a $C_{0}$-semigroup in terms of…