Related papers: Prym-Tyurin varieties using self-products of group…

We give an irreducible decomposition of the so-called local representations (see arXiv:0707.2151) of the quantum Teichm\"uller space $\mathcal{T}_q(\Sigma)$ where $\Sigma$ is a punctured surface of genus $g>0$ and $q$ is a primitive $N$-th…

In recent years there has been an interest in constructing examples of closed Riemann surfaces whose jacobian varieties are isogenous to a product of many elliptic factors and some other jacobian varieties. The first ones, provided by…

In the first part of the paper, we give an explicit algorithm to compute the (genus zero) Gromov-Witten invariants of blow-ups of an arbitrary convex projective variety in some points if one knows the Gromov-Witten invariants of the…

In this paper, we consider the construction of irreducible representations of finite pattern groups in terms of Panov's associative polarization, which is a finite-field analogue of Kirillov's orbital method. Using this construction, first,…

Given a non-isotrivial elliptic curve over $\mathbb{Q}(t)$ with large Mordell-Weil rank, we explain how one can build, for suitable small primes $p$, infinitely many fields of degree $p^2-1$ whose ideal class group has a large $p$-torsion…

To follow up on the results of [1], we propose a computationally efficient explicit cyclic decomposition of the maximal tori in the groups $SL_n(q)$ and $SU_n(q)$ and their projective images. We also derive some corollaries to simplify…

We prove several results on the model theory of Artin groups, focusing on Artin groups which are ``far from right-angled Artin groups''. The first result is that if $\mathcal{C}$ is a class of Artin groups whose irreducible components are…

Given an Enriques surface $T$, its universal K3 cover $f: S\to T$, and a genus $g$ linear system $|C|$ on $T$, we construct the relative Prym variety $P_H=\Prym_{v, H}(\D/\CC)$, where $\CC\to |C|$ and $\D\to |f^*C|$ are the universal…

Let Q be a Dynkin quiver, and let P(Q) be the corresponding preprojective algebra. Let I be a set of pairwise different indecomposable irreducible components of varieties of P(Q)-modules such that generically there are no extensions between…

Let $\mathcal{X}$ be a (projective, geometrically irreducible, nonsingular) algebraic curve of genus $g \ge 2$ defined over an algebraically closed field $\mathbb{K}$ of odd characteristic $p\ge 0$, and let $\rm{Aut}(\mathcal{X})$ be the…

Block and G\"ottsche have defined a $q$-number refinement of counts of tropical curves in $\mathbb{R}^2$. Under the change of variables $q=e^{iu}$, we show that the result is a generating series of higher genus log Gromov-Witten invariants…

We explicitly construct the Kummer variety associated to the Jacobian of a hyperelliptic curve of genus 3 that is defined over a field of characteristic not equal to 2 and has a Weierstra{\ss} point defined over the same field. We also…

We give a method to construct new self-adjoint representations of the braid group. In particular, we give a family of irreducible self-adjoint representations of dimension arbitrarily large. Moreover we give sufficient conditions for a…

Kirillov's orbit theory provides a powerful tool for the investigation of irreducible unitary representations of many classes of Lie groups. In a previous paper we used a modification hereof, called monomial linearisation, to construct a…

Let $q$ be a power of a prime $p$, $G$ be a finite abelian group, where $p$ does not divide $|G|$,and let $n$ be a positive integer. In this paper we find a formula for the number of irreducible representations of $G$ of a given dimension…

For $i\geq2$, we compute the first coefficients of the class $[\overline{D}(\mu;3)]$ in the rational Picard group of the moduli of Prym curves $\overline{\mathcal{R}}_{2i}$, where $D(\mu;3)$ is the divisor parametrizing pairs $[C,\eta]$ for…

The classical definition of Prym varieties deals with the unramified covers of curves. The aim of the present paper is to give explicit algebraic descriptions of the Prym varieties associated to ramified double covers of algebraic curves.…

We use recently developed algorithms and a new database of modular curves constructed for the L-functions and Modular Forms Database to enumerate completely decomposable modular Jacobians of level N < 240. In particular, we find examples in…

Given an integer $D$ and an ordinary isogeny class of abelian varieties defined over a finite field $\mathbb{F}_q$ with commutative $\mathbb{F}_q$-endomorphism algebra, we provide algorithms for computing all isogenies of degree dividing…

In this paper, we study the kernels of the $\mathrm{SO}(3)$-Witten-Reshetikhin-Turaev quantum representations $\rho_p$ of mapping class groups of closed orientable surfaces $\Sigma_g$ of genus $g.$ We investigate the question whether the…