Related papers: Analytic classification of plane branches up to mu…

The author determines the structure of automorphism groups of smooth plane curves of degree at least four. Furthermore, he gives some upper bounds for the order of automorphism groups of smooth plane curves and classifies the cases with…

We give a geometric classification of 4-dimensional superalgebras over an algebraic closed field.

We classify affine varieties with an action of a connected, reductive algebraic group such that the group is isomorphic to an open orbit in the variety. This is accomplished by associating a set of one-parameter subgroups of the group to…

We compute log canonical thresholds of reduced plane curves of degree $d$ at points of multiplicity $d-1$. As a consequence, we describe all possible values of log canonical threshold that are less than $2/(d-1)$ for reduced plane curves of…

The fine abelian group gradings on the simple classical Lie algebras (including D4) over algebraically closed fields of characteristic 0 are determined up to equivalence. This is achieved by assigning certain invariant to such gradings that…

We compute numerically the homology of several graph complexes in low loop orders, extending previous results.

We present a complete computational classification of the combinatorial types of hyperplane sections, or slices, of the regular cube up to dimension six. For each dimension, we determine the exact number of distinct combinatorial types.…

In the present paper we obtain the list of algebras, up to isomorphism, such that closure of any complex finite-dimensional algebra contains one of the algebra of the given list.

We classify the conjugacy classes of minimally ramified nonabelian subgroups of order 8 in the Nottingham group $N(F_4)$. We then use finite automata to give explicit descriptions of representatives for each of these conjugacy classes.

On any smooth $n$-dimensional variety we give a pretty precise picture of rank $r$ Ulrich vector bundles with numerical dimension at most $\frac{n}{2}+r-1$. Also, we classify non-big Ulrich vector bundles on quadrics and on the Del Pezzo…

This paper is devoted to study multiplicity and regularity as well as to present some classifications of complex analytic sets. We present an equivalence for complex analytical sets, namely blow-spherical equivalence and we receive several…

We construct a good compactification of the variety of irreducible projective plane curves of degree n with d nodes and no other singularities.

We present algorithms for parametrizing by radicals an irreducible curve, not necessarily plane, when the genus is less o equal to 4 and they are defined over an algebraically closed field of characteristic zero. In addition, we also…

Using only undergraduate-level methods, we classify all groups of order $p^4$, where $p$ is an odd prime.

We show that for every g > 1 there is a compact arithmetic Riemann surface of genus g with at least 4(g-1) automorphisms, and that this lower bound is attained by infinitely many genera, the smallest being 24.

We describe the images of multilinear polynomials of degree up to four on the upper triangular matrix algebra.

The split quartic Cayley algebra is a structurable algebra which has been used to give constructions of Lie algebras of type D4. Here, we calculate its group of automorphisms, its algebra of derivations and its gradings.

The group gradings on the symmetric composition algebras over arbitrary fields are classified. Applications of this result to gradings on the exceptional simple Lie algebras are considered too.

We develop categorical and number theoretical tools for the classification of super-modular categories. We apply these tools to obtain a partial classification of super-modular categories of rank $8$. In particular we find three distinct…

We classify small binary bibraces, using the correspondence with alternating algebras over the field F2, up to dimension eight, also determining their isomorphism classes. These finite-dimensional algebras, defined by an alternating…