Related papers: On exceptional terminal singularities

We give new examples of terminal and log canonical singularities.

This is the first of a series of papers studying real algebraic threefolds using the minimal model program. The main results are outlined in Part II. The present part I. contains the necessary preliminary work concerning terminal…

We prove that nine-dimensional exceptional quotient singularities exist.

The purely log terminal blow-ups of three-dimensional terminal toric singularities are described.

In [8] we found a class of overlapping asymmetric self-similar measures on the real line, which are generically absolutely continuous with respect to the Lebesgue measure. Here we construct exceptional measures in this class being singular.

New types of maximal symplectic partial spreads are constructed.

We study the systems of ordinary differential equations which are implicit with respect to the higher derivatives, appearing in the linear form, and their solutions near the singular points. The invertibility of the higher derivatives…

A finitely generated solvable group with unbounded iterated identity is constructed.

We construct the first examples of residually finite non-exact groups. The construction is based on author's earlier construction of groups containing isometrically expanders using a graphical small cancellation.

In the article, we exhibit a series of new examples of rigid plane curves, that is, curves, whose collection of singularities determines them almost uniquely up to a projective transformation of the plane.

In this paper, using the similarity method, we construct particular solutions with singularities for degenerate high-order equations. The considered equations have singularities of the first and second kind. Particular solutions are…

We prove astonishing identities generated by compositions of positive integers. In passing, we obtain two new identities for Stirling numbers of the first kind. In the two last sections we clarify an algebraic sense of these identities and…

We show that constructible models of arbitrary complete continuous first-order theories are unique up to isomorphism.

Singularities appear in numerous important mathematical models used in Physics. And in most of such cases singularities are involved in essentially nonlinear contexts. For more than four decades, general enough nonlinear theories of…

Particular solutions of the Benney equations are constructed. Their properties are discussed.

Based on the proposed unifying theory of dark matter and quintessence, a novel nonlinear structure formation scenario is suggested. This top-down singular and turbulent scenario results in a bottom-up hierarchical clustering and is…

The properties of finite lumps of strange quark matter (strangelets) with emphasis on the two scenarios of producing strange matter in relativistic heavy ion collisions are summarized. As an outlook, the possibility of short-lived strange…

We construct periodic monopoles (with singularities), i.e. monopoles on $\mathbb{R}^{2} \times \mathbb{S}^{1}$ possibly singular at a finite collection of points, by gluing methods.

We construct highly singular projective curves and surfaces defined by invariants of primitive complex reflection groups.

In the present paper, we give some examples of stochastic differential equations which have delicateness in the Markov and strong Markov properties, the uniqueness locally in time and globally in time, and initial conditions. Moreover, we…