Related papers: Baker-Akhiezer Modules on Rational Varieties

The restriction, on the spectral variables, of the Baker-Akhiezer (BA) module of a g-dimensional principally polarized abelian variety with the non-singular theta divisor to an intersection of shifted theta divisors is studied. It is shown…

In this work, we construct commutative rings of two variable matrix differential operators that are isomorphic to a ring of meromorphic functions on a rational manifold obtained from the $CP^1\times CP^1$ by identification of two lines with…

We introduce the notion of discrete Baker-Akhiezer (DBA) modules, which are modules over the ring of difference operators, as a certain discretization of Baker-Akhiezer modules which are modules over the ring of differential operators. We…

We enumerate smooth rational curves on very general Weierstrass fibrations over hypersurfaces in projective space. The generating functions for these numbers lie in the ring of classical modular forms. The method of proof uses topological…

In this paper we study Baker-Akhiezer spinor kernel on moduli spaces of meromorphic differentials on Riemann surfaces. We introduce the Baker-Akhiezer tau-function which is related to both Bergman tau-function (which was studied before in…

For every prime $p$, Mohan Kumar constructed examples of stably free modules of rank $p$ on suitable $(p+1)$-dimensional smooth affine varieties. This note discusses how to detect the corresponding unimodular rows in motivic cohomology.…

Let $X$ be a variety over a complete nontrivially valued field $K$. We construct an algebraizable formal model for the analytification of $X$ in the case $X$ admits a closed embedding into a toric variety. By algebraizable we mean that the…

In this paper, we extend the characterization of $\mathbb{Z}[x]/\ < f \ >$, where $f \in \mathbb{Z}[x]$ to be a free $\mathbb{Z}$-module to multivariate polynomial rings over any commutative Noetherian ring, $A$. The characterization allows…

In this paper we show that if two central simple $k$-algebras generate the same cyclic subgroup in $\mathrm{Br}(k)$, then there are rational maps between varieties associated to these algebras, such as Brauer--Severi varieties, norm…

We study algebras of meromorphic modular forms whose poles lie on Heegner divisors for orthogonal and unitary groups associated to root lattices. We give a uniform construction of $147$ hyperplane arrangements on type IV symmetric domains…

For a rational function of several variables with nonnegative imaginary part on the upper poly-half-plane, the matrix representations are obtained.

We present bases for certain spaces of meromorphic vector-valued rational-weight mock modular forms constructed using Rademacher sums.

We study linear ordinary differential equations which are analytically parametrized on Hermitian symmetric spaces and invariant under the action of symplectic groups. They are generalizations of the classical Lam\'e equation. Our main…

A new basis for the polynomial ring of infinitely many variables is constructed which consists of products of Schur functions and Q-functions. The transition matrix from the natural Schur function basis is investigated.

K\"ahler-Poisson algebras were introduced as algebraic analogues of function algebras on K\"ahler manifolds, and it turns out that one can develop geometry for these algebras in a purely algebraic way. A K\"ahler-Poisson algebra consists of…

We discuss an interesting duality known to occur for certain complex reflection groups, namely the duality groups. Our main construction yields a concrete, representation theoretic realisation of this duality. This allows us to naturally…

We introduce and study modular truncations of the Ackermann function viewed as self-maps on finite rings. These maps form a hierarchy of rapidly increasing compositional complexity indexed by recursion depth. We investigate their structural…

The moduli space of algebraic foliations on P2 of a fixed degree and with a center singularity has many irreducible components. We find a basis of the Brieskorn module defined for a rational function and prove that set of pull-back…

We study the parametrizations of simple modules provided by the theory of basic sets for all finite Weyl groups. In the case of type B, we show the existence of basic sets for the matrices of constructible representations. Then we study…

We construct smooth rational real algebraic varieties of every dimension $\ge$ 4 which admit infinitely many pairwise non-isomorphic real forms.