Related papers: On the log minimal model program for irreducible s…

In this short note, we consider the conjecture that the log canonical divisor (resp. the anti-log canonical divisor) $K_X + \Delta$ (resp. $-(K_X + \Delta)$) on a pair $(X, \Delta)$ consisting of a complex projective manifold $X$ and a…

Birkar and Hu showed that if a pair $(X,\Delta)$ is lc and $K_{X}+\Delta$ admits a birational Zariski decomposition, then $(X,\Delta)$ has a minimal model. Analogously, we prove that if a pair $(X,\Delta)$ is pklt and $-(K_{X}+\Delta)$…

We use the theory of motivic integration for singular spaces to give a characterization of minimal log discrepencies in terms of the codimension of certain subsets of spaces of arcs. This is done for arbitrary pairs $(X,Y)$, with $X$ normal…

Let $(X\ni x,B)$ be an lc surface germ. If $X\ni x$ is klt, we show that there exists a divisor computing the minimal log discrepancy of $(X\ni x,B)$ that is a Koll\'ar component of $X\ni x$. If $B\not=0$ or $X\ni x$ is not Du Val, we show…

We establish the minimal model program for log canonical and Q-factorial surfaces over excellent base schemes.

In the present paper we continue the programme of systematic construction of invariant differential operators on the example of the non-compact groups Sp(n,R). Earlier in arXiv:1205.5521 we gave the main multiplets and the main reduced…

We consider resolvent splitting algorithms for finding a zero of the sum of finitely many maximally monotone operators. The standard approach to solving this type of problem involves reformulating as a two-operator problem in the…

We prove that semialgebraic sets of rectangular matrices of a fixed rank, of skew-symmetric matrices of a fixed rank and of real symmetric matrices whose eigenvalues have prescribed multiplicities are minimal submanifolds of the space of…

Motivated by Stanley's results in \cite{St02}, we generalize the rank of a partition $\lambda$ to the rank of a shifted partition $S(\lambda)$. We show that the number of bars required in a minimal bar tableau of $S(\lambda)$ is max$(o, e +…

Given a fibration of a symplectic manifold by lagrangian tori, we show that each symplectic vector field splits into two parts : the first is Hamiltonian and the second is symplectic and preserves the fibration. We then show an application…

Extracting isolated rays from a symplectic manifold result in a manifold symplectomorphic to the initial one. The same holds for higher dimensional parametrized rays under an additional condition. More precisely, let $(M,\omega)$ be a…

For a finite dimensional symplectic manifold $(M,\omega)$ with a symplectic form $\omega$, corresponding loop space ($LM=C^\infty(S^1,M)$) admits a weak symplectic form $\Omega^\omega$. We prove that the loop space over $\mbr^n$ admits…

We prove that cocompact arithmetic lattices in a simple Lie group are uniformly discrete if and only if the Salem numbers are uniformly bounded away from $1$. We also prove an analogous result for semisimple Lie groups. Finally, we shed…

We prove that the group of Hamiltonian automorphisms of a symplectic 4-manifold contains only finitely many conjugacy classes of maximal compact tori with respect to the action of the full symplectomorphism group. We also extend to rational…

We develop differential and symplectic geometry of differentiable Deligne-Mumford stacks (orbifolds) including Hamiltonian group actions and symplectic reduction. As an application we construct new examples of symplectic toric DM stacks as…

An important step in the efficient computation of multi-dimensional theta functions is the construction of appropriate symplectic transformations for a given Riemann matrix assuring a rapid convergence of the theta series. An algorithm is…

In this paper we establish a Nadel-type vanishing theorem and a Kawamata--Viehweg-type vanishing theorem concerning the asymptotic multiplier ideal sheaf on a compact K\"{a}hler manifold $X$. After that, we provide a relative variant.

Let $X$ be a projective Frobenius split variety over an algebraically closed field with splitting $\theta : F_* \O_X \to \O_X$. In this paper we give a sharp bound on the number of subvarieties of $X$ compatibly split by $\theta$. In…

Numerous problems in optics, quantum physics, stability analysis, and control of dynamical systems can be brought to an optimization problem with matrix variable subjected to the symplecticity constraint. As this constraint nicely forms a…

In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact algebras $su(n,n)$. Earlier were given the main multiplets of indecomposable elementary…