We prove that certain Severi varieties of nodal curves positive genus on general blow-ups the twofold symmetric product a elliptic curve are non-empty and smooth expected dimension. This result, besides its intrinsic value, is an important preliminary step for proof nonemptiness Enriques surfaces in arXiv:2109.10735.

in this paper we introduce two symmetric variants of amenability, symmetric module amenability and symmetric connes amenability. we determine symmetric module amenability and symmetric connes amenability of some concrete banach algebras. indeed, it is shown that $ell^1(s)$ is  a symmetric $ell^1(e)$-module amenable if and only if $s$ is amenable, where $s$ is an inverse semigroup with subsemigr...

Symmetric pattern-avoiding permutations are restricted permutations which are invariant under actions of certain subgroups of D4, the symmetry group of a square. We examine pattern-avoiding permutations with 180◦ rotational-symmetry. In particular, we use combinatorial techniques to enumerate symmetric permutations which avoid one pattern of length three and one pattern of length four. Our resu...

We prove that the problems of classifying triples of symmetric or skew-symmetric matrices up to congruence, local commutative associative algebras with zero cube radical and square radical of dimension 3, and Lie algebras with central commutator subalgebra of dimension 3 are hopeless since each of them reduces to the problem of classifying pairs of n-by-n matrices up to simultaneous similarity....

Let G/K be a simply connected spin compact inner irreducible symmetric space, endowed with the metric induced by the Killing form of G sign-changed. We give a formula for the square of the first eigenvalue of the Dirac operator in terms of a root system of G. As an example of application, we give the list of the first eigenvalues for the spin compact irreducible symmetric spaces endowed with a ...