Related papers: Counting square free monomial cremona maps
We propose a new method to study birational maps between Fano varieties based on multiplier ideal sheaves. Using this method, we prove equivariant birational rigidity of four Fano threefolds acted on by the group A6. As an application, we…
We discuss a simulation algorithm for dynamical fermions, which combines the multiboson technique with the Hybrid Monte Carlo algorithm. The algorithm turns out to give a substantial gain over standard methods in practical simulations and…
We use generating functions over group rings to count polynomials over finite fields with the first few coefficients prescribed and a factorization pattern prescribed. In particular, we obtain different exact formulas for the number of…
We present a set of Feynman integrals appearing in calculations of different QED processes to the one-loop accuracy. We consider scalar, vector, and tensor integrals with two, three, four and five denominators. The cases of equal and…
Given a symmetric variety Y defined over the rationals and a non-zero polynomial with integer coefficients, we use techniques from homogeneous dynamics to establish conditions under which the polynomial can be made r-free for a Zariski…
A square-free integer is a positive integer that is not divisible by the square of any prime. Merten's function, $M(x)$ is defined as the difference between the number of square free integers with an even number of prime factors and the…
A Cremona transformation is a birational self-map of the projective space $ \mathbb{P}^{n} $. Cremona transformations of $ \mathbb{P}^{n} $ form a group and this group has a rational action on subvarieties of $ \mathbb{P}^{n} $ and hence on…
We obtain the trace map image of the values of certain harmonic volumes for some quotients of Fermat curves. This provides the algorithm that the algebraic cycles called by the k-th Ceresa cycles are not algebraically equivalent to zero in…
The short note is devoted to the setting free of hidden symmetries in Verma modules over sl(2,C) by the noncommutative Veronese mappings.
We present a set of related Hybrid Monte Carlo methods to simulate an arbitrary number of dynamical overlap fermions. Each fermion is represented by a chiral pseudo-fermion field. The new algorithm reduces critical slowing down in the…
This paper is the first in a sequence on the structure of sets of solutions to systems of equations over a free associative algebra. We start by constructing a Makanin-Razborov diagram that encodes all the homogeneous solutions to a…
In this work, we study a family of Cremona transformations of weighted projective planes which generalize the standard Cremona transformation of the projective plane. Starting from special plane projective curves we construct families of…
Least-squares optimized polynomials are discussed which are needed in the two-step multi-bosonic algorithm for Monte Carlo simulations of quantum field theories with fermions. A recurrence scheme for the calculation of necessary…
We discuss efficient conversion algorithms for orthogonal polynomials. We describe a known conversion algorithm from an arbitrary orthogonal basis to the monomial basis, and deduce a new algorithm of the same complexity for the converse…
Cumulant mapping employs a statistical reconstruction of the whole by sampling its parts. The theory developed in this work formalises and extends ad hoc methods of `multi-fold' or `multi-dimensional' covariance mapping. Explicit formulae…
A direct proof is given here which shows that instead of 6 complex numbers, the triangular mass matrix for each sector could just be expressed in terms of 5 by performing a specific weak basis transformation, leading therefore to a new…
We give a method to obtain, from Voiculescu's inequality, norm estimates for sums of free variables with amalgamation in general fully symmetric spaces. We use these estimates to interpolate the Burkholder inequalities for non commutative…
In this paper, we consider two basic questions about presenting a homogeneous polynomial f: how many variables are needed for presenting f? How can one find a presentation of f involving as few variables as possible? We give a complete…
Let K be a field and S a polynomial ring in a finite number of variables over K. Let F be a finitely generated graded free S-module. We examine some classes of squarefree monomial submodules of F. Hence, we focalize our attention on the…
We present a general approach to greatly increase at little cost the efficiency of Monte Carlo algorithms. To each observable to be computed we associate a renormalized observable (improved estimator) having the same average but a different…