Related papers: Classification of threefold enc cDV quotient singu…
It is proved that a three-dimensional double cone is a birationally rigid variety. We also compute the group of birational automorphisms of such a variety. This work is based on the method of "untwisting" maximal singularities of linear…
In this paper, we define and study Clifford quadratic complete intersections. After showing some properties of Clifford quantum polynomial algebras, we show that there is a natural one-to-one correspondence between Clifford quadratic…
Positively graded algebras are fairly natural objects which are arduous to be studied. In this article we query quotients of non-standard graded polynomial rings with combinatorial and commutative algebra methods.
We complete the explicit study of a three-fold divisorial contraction whose exceptional divisor contracts to a point, by treating the case where the point downstairs is a singularity of index $n \ge 2$. We prove that if this singularity is…
In this paper we classify, up to rigid isotopy, non-singular real rational curves of degrees less than or equal to 6 in a quadric homeomorphic to the 3-sphere. We also study their connections with rigid isotopy classes of real rational…
We show that there exists a cubic threefold defined by an invertible polynomial that, when quotiented by the maximal diagonal symmetry group, has a derived category which does not have a full exceptional collection consisting of line…
This paper is concerned with the local bifurcation analysis around typical singularities of piecewise smooth planar dynamical systems. Three-parameter families of a class of non$-$smooth vector fields are studied and the tridimensional…
We construct a large class of projective threefolds with one node (aka non-degenerate quadratic singularity) such that their small resolutions are not projective.
We evaluate the enumerative invariants of low degree on the mirror quintic threefold.
Casorati determinant solution to the non-autonomous discrete KdV equation is constructed by using the bilinear formalism. We present three different bilinear formulations which have different origins.
We show that the integrable subclassess of a class of third order non-autonomous equations are identical with the integrable subclassess of the autonomous ones.
We give a complete classification in canonical forms on finite-dimensional vector spaces over the real numbers.
In this paper we study singularities of third secant varieties of Veronese embedding $v_d(\mathbb{P}^n)$, which corresponds to the variety of symmetric tensors of border rank at most three in $(\mathbb{C}^{n+1})^{\otimes d}$.
The paper deals with a construction of a separating system of rational invariants for finite dimensional generic algebras. In the process of dealing an approach to a rough classification of finite dimensional algebras is offered by…
A classification of discrete integrable systems on quad-graphs, i.e. on surface cell decompositions with quadrilateral faces, is given. The notion of integrability laid in the basis of the classification is the three-dimensional…
We describe the possible Mordell-Weil groups for degree 1 elliptic threefold with rational base and constant $j$-invariant. Moreover, we classify all such elliptic threefolds if the $j$-invariant is nonzero. We can use this classification…
In this article we study the analytic classification of certain types of quasi-homogeneous cuspidal holomorphic foliations in $(\CC^3,{\bf 0})$ via the essential holonomy defined over one of the components of the exceptional divisor that…
Quantum Euclidean spaces, as Moyal deformations of Euclidean spaces, are the model examples of noncompact noncommutative manifold. In this paper, we study the quantum Euclidean space equipped with partial derivatives satisfying canonical…
We define and calculate the weighted multiplicities of non Gorenstein terminal singularities on threefolds and some quotient singularities. We improve freeness conditions on threefolds.
Cubic invariants for two-dimensional Hamiltonian systems are investigated using the Jacobi geometrization procedure. This approach allows for a unified treatment of invariants at both fixed and arbitrary energy. In the geometric picture the…