Related papers: Pruned double Hurwitz numbers
We shall consider the product of complex random matrices from the independent complex Ginibre ensembles. The product includes complex matrices $Z_i, Z_i^\dagger, \, i = 1, \ldots, n$ and $2n$ sources (complex matrices $C_i$ and $C_i^*$).…
We provide a direct correspondence between the $b$-Hurwitz numbers with $b=1$ from \cite{ChapuyDolega}, and twisted Hurwtiz numbers from \cite{TwistedHurwitz}. This provides a description of real coverings of the sphere with ramification on…
We expand Topological Field Theory on some special CW-complexes (brane complexes). This Brane Topological Field Theory one-to-one corresponds to infinite dimensional Frobenius Algebras, graduated by CW-complexes of lesser dimension. We…
The study of the moduli of covers of the projective line leads to the theory of Hurwitz varieties covering configuration varieties. Certain one-dimensional slices of these coverings are particularly interesting Belyi maps. We present…
Goulden, Jackson and Vakil observed a polynomial structure underlying one-part double Hurwitz numbers, which enumerate branched covers of $\mathbb{CP}^1$ with prescribed ramification profile over $\infty$, a unique preimage over 0, and…
We propose a new, conjectural recursion solution for Hurwitz numbers at all genera. This conjecture is based on recent progress in solving type B topological string theory on the mirrors of toric Calabi-Yau manifolds, which we briefly…
Hurwitz (1887) defined a continued fraction algorithm for complex numbers which is better behaved in many respects than a more "natural" extension of the classical continued fraction algorithm to the complex plane would be. Although the…
We study a generalization of the Harish-Chandra - Itzykson - Zuber integral to tensors and its expansion over trace-invariants of the two external tensors. This gives rise to natural generalizations of monotone double Hurwitz numbers, which…
The canonical covering maps from Hurwitz varieties to configuration varieties are important in algebraic geometry. The scheme-theoretic fiber above a rational point is commonly connected, in which case it is the spectrum of a Hurwitz number…
We investigate the universal Jacobian of degree n line bundles over the Hurwitz stack of double covers of P^1 by a curve of genus g. Our main results are: the construction of a smooth, irreducible, universally closed (but not separated)…
We consider multi-matrix models that are generating functions for the numbers of branched covers of the complex projective line ramified over $n$ fixed points $z_i$, $i=1,\dots,n$, (generalized Grotendieck's dessins d'enfants) of fixed…
We prove an analogue of the Riemann-Hurwitz theorem for computing Euler characteristics of pullbacks of coherent sheaves through finite maps of smooth projective varieties, subject only to the condition that the irreducible components of…
Let $\pi : Y \to X$ be a branched $\mathbf{Z}/p \mathbf{Z}$-cover of smooth, projective, geometrically connected curves over a perfect field of characteristic $p>0$. We investigate the relationship between the $a$-numbers of $Y$ and $X$ and…
We use a rigidity argument to prove the existence of two related degree twenty-eight covers of the projective plane with Galois group SU3(3).2 = G2(2). Constructing corresponding two-parameter polynomials directly from the defining…
An almost Belyi covering is an algebraic covering of the projective line, such that all ramified points except one simple ramified point lie above a set of 3 points of the projective line. In general, there are 1-dimensional families of…
We study the ramified Prym map $\mathcal P_{g,r} \longrightarrow \mathcal A_{g-1+\frac r2}^{\delta}$ which assigns to a ramified double cover of a smooth irreducible curve of genus $g$ ramified in $r$ points the Prym variety of the…
Spin Hurwitz numbers count ramified covers of a spin surface, weighted by the size of their automorphism group (like ordinary Hurwitz numbers), but signed $\pm 1$ according to the parity of the covering surface. These numbers were first…
We prove that a double cover of $\mathbb{P}^2$ ramified along a general smooth curve B of degree $2s$, for $s \geq 3$, supports a rank 2 special Ulrich bundle.
In a recent paper, Adamchik [V.S. Adamchik, On the Hurwitz function for rational arguments, Appl. Math. Comp. 187 (2007) 3--12] expressed in a closed form symbolic derivatives of four functions belonging to the class of functions whose…
In this paper we study various aspects of the double ramification (DR) hierarchy, introduced by the first author, and its quantization. We extend the notion of tau-symmetry to quantum integrable hierarchies and prove that the quantum DR…