Related papers: Factorization semigroups and irreducible component…

We show the simple Hurwitz space $\mathcal{H}_{g,d}$ has trivial rational Picard group for $d>g-1$ and is uniruled for $d>g+1$.

We prove that any two irreducible cuspidal Hurwitz curves $C_0$ and $C_1$ (or more generally, curves with A-type singularities) in the Hirzebruch surface $F_N$ with coinciding homology classes and sets of singularities are regular…

We describe the centralizer of irreducible representations from a finitely generated group $\Gamma$ to $PSL(p,\mathbb{C})$ where $p$ is a prime number. This leads to a description of the singular locus (the set of conjugacy classes of…

This paper is a sequel to [He7]. There a notion of marking of isolated hypersurface singularities was defined, and a moduli space $M_\mu^{mar}$ for marked singularities in one $\mu$-homotopy class of isolated hypersurface singularities was…

Parametric families in the centre ${\bf Z}({\bf C}[S_n])$ of the group algebra of the symmetric group are obtained by identifying the indeterminates in the generating function for Macdonald polynomials as commuting Jucys-Murphy elements.…

Let $f(x)$ be a monic polynomial in $\dZ[x]$ with no rational roots but with roots in $\dQ_p$ for all $p$, or equivalently, with roots mod $n$ for all $n$. It is known that $f(x)$ cannot be irreducible but can be a product of two or more…

We prove that a resolution of singularities of any finite covering of the projective plane branched along a Hurwitz curve $\bar H$ and, maybe, along a line "at infinity" can be embedded as a symplectic submanifold into some projective…

We determine the irreducible components of Igusa varieties for Shimura varieties of Hodge type under a mild condition and use that to compute the irreducible components of central leaves. In particular, we show that a strong version of the…

We prove that the $\mathrm{Sp}(1)$-Seiberg-Witten equation over a closed hyperbolic $3$-manifold ${\mathbb H}^3/\Gamma$ always admits a canonical irreducible solution induced by the hyperbolic metric. We also prove that the Zariski tangent…

Sect 1 introduces Nielsen classes attached to (G,C), where C is r conjugacy classes in a finite group G, and a braid action on them. These give reduced Hurwitz spaces, denoted H(G,C)^rd. The section concludes with a braid formula for the…

If in a given rank $r$, there is an irreducible complex local system with torsion determinant and quasi-unipotent monodromies at infinity on a smooth quasi-projective variety, then for every prime number $\ell$, there is an absolutely…

For an integral domain $R$ and a commutative cancellative monoid $M$, the ring consisting of all polynomial expressions with coefficients in $R$ and exponents in $M$ is called the monoid ring of $M$ over $R$. An integral domain is called…

A unitary representation of a, possibly infinite dimensional, Lie group $G$ is called semibounded if the corresponding operators $i\dd\pi(x)$ from the derived representation are uniformly bounded from above on some non-empty open subset of…

In this paper, we study some aspects of the irreducibility of $\widetilde{M_g^{Pl}(G)}$ and its interrelation with the existence of "normal forms", i.e. non-singular plane equations (depending on a set of parameters) such that a…

In this article we prove that the arithmetic profinite iterated monodromy group of a post-critically infinite unicritical polynomial is regular branch (and so of positive Hausdorff dimension), and has positive fixed-point proportion when…

In "Curves on Heisenberg invariant quartic surfaces in projective 3-space", Eklund showed that a general $(\mathbb{Z}/2\mathbb{Z})^{4}$-invariant quartic K3 surface contains at least $320$ conics. In this paper we analyse the field of…

In chapter 1 we define period mappings of Hodge-de Rahm type for certain submersive, yet not necessarily locally topologically trivial, morphisms of complex manifolds. Generalizing Griffiths's theory, we interpret the differential of such…

For $w$ in the symmetric group $S_n$, let $\widetilde C_w$ be the corresponding modified, signless Kazhdan--Lusztig basis element of the type-$A$ Hecke algebra $H_n(q)$. An extension [Ann. Comb. 25, no. 3 (2021) pp. 757--787] of a result of…

Using $p$-adic local Langlands correspondence for $\operatorname{GL}_2(\mathbb{Q}_2)$ and an ordinary $R = \mathbb{T}$ theorem, we prove that the support of patched modules for quaternionic forms meet every irreducible component of the…

Main Theorem: Spaces of r-branch point 3-cycle covers, degree n or Galois of degree n!/2 have one (resp. two) component(s) if r=n-1 (resp. r\ge n). Improves Fried-Serre on deciding when sphere covers with odd-order branching lift to…