Related papers: Brill's equations as a GL(V)-module

In \cite{Cho09}, Choi studied congruences of coefficients (modulo $T^q-T$) for Drinfeld modular forms of level $\Gamma_0(T)$, trivial type and the linear relations between the initial coefficients of those. In this article, we generalize…

Based on Balmer's tensor triangular Chow group, we propose K-theoretic Chow groups of derived categories of noetherian schemes and their Milnor variants for regular schemes and their thickenings. We discuss functoriality and show that our…

We study the semi-decomposable invariants of a split semisimple group and their extension to a split reductive group by using the torsion in the codimension $2$ Chow groups of a product of Severi-Brauer varieties. In particular, for any…

We give a presentation for the Chow ring of the moduli space of degree two stable maps from two-pointed rational curves to P^1. Also, integrals of of all degree four monomials in the hyperplane pullbacks and boundary divisors of this ring…

We consider a certain mixed polynomial which is an extended Lens equation $L_{n,m}=\bar z^m-p(z)/q(z)$ with $\text{degree}\, q=n$, $\text{degree}\, p<n$ whose numerator is a mixed polynomial of degree $(n+m;n,m)$. Then we consider its…

Motivated by the computation of the BPS-invariants on a local Calabi-Yau threefold suggested by S. Katz, we compute the Chow ring and the cohomology ring of the moduli space of stable sheaves of Hilbert polynomial $4m+1$ on the projective…

We provide a general method for computing rational Chow rings of moduli of smooth complete intersections. We specialize this result in different ways: to compute the integral Picard group of the associated stack ; to obtain an explicit…

A general method of obtaining linear differential equations having polynomial solutions is proposed. The method is based on an equivalence of the spectral problem for an element of the universal enveloping algebra of some Lie algebra in the…

The modular decomposition is a technique that applies but is not restricted to graphs. The notion of module naturally appears in the proofs of many graph theoretical theorems. Computing the modular decomposition tree is an important…

We construct plane models of the modular curve $X_H(\ell)$, and use their explicit equations to compute Galois representations associated to modular forms for values of $\ell$ that are significantly higher than in prior works.

We study the notion of a birational Chow-K\"unneth decomposition, which is essentially a decomposition of the integral birational motive of a variety. The existence of a birational Chow-K\"unneth decomposition is stably birationally…

Let $f : X \rightarrow B$ be a proper flat dominant morphism between two smooth quasi-projective complex varieties $X$ and $B$. Assume that there exists an integer $l$ such that all closed fibres $X_b$ of $f$ satisfy $CH_j(X_b) = \Q$ for…

We propose an explicit and practical algorithm for computing Galois conjugates and irreducible polynomials for special values of modular functions evaluated at CM points associated with imaginary quadratic orders. Our approach builds upon…

We study the Chow ring of the moduli stack $\mathfrak{M}_{g,n}$ of prestable curves and define the notion of tautological classes on this stack. We extend formulas for intersection products and functoriality of tautological classes under…

We present a combinatorial monomial basis (or, more precisely, a family of monomial bases) in every finite-dimensional irreducible $\mathfrak{so}_{2n+1}$-module. These bases are in many ways similar to the FFLV bases for types $A$ and $C$.…

We compute the Chow rings with integral coefficients of moduli stacks of minimal Weierstrass fibrations over the projective line. For each integer $N\geq 1$, there is a moduli stack $\mathcal{W}^{\mathrm{min}}_N$ parametrizing minimal…

A presentation of a degree $d$ form in $n+1$ variables as the sum of homogenous elements ``essentially'' involving $n$ variables is called a {\em codimension one decomposition}. Codimension one decompositions are introduced and the related…

In this paper we investigate Murre's conjecture on the Chow--K\"unneth decomposition for two classes of examples. We look at the universal families of smooth curves over spaces which dominate the moduli space $\cM_g$, in genus at most 8 and…

We prove that the irreducible decomposition of the permutation representation of GL(n,q) on GL(n,q)/GL(n-m,q) stabilizes for large n. We deduce, as a consequence, a representation stability theorem for finitely generated VIC-modules.

We study the deformations of the Chow group of zero-cycles of the special fibre of a smooth scheme over a henselian discrete valuation ring. Our main tools are Bloch's formula and differential forms. As a corollary we get an algebraization…