Related papers: Anticanonical minimal models and Zariski decomposi…

Let \Delta be the Okounkov body of a divisor D on a projective variety X. We describe a geometric criterion for \Delta to be a lattice polytope, and show that in this situation X admits a flat degeneration to the corresponding toric…

Let $X$ be a minimal projective 3-fold of general type. The pluricanonical section index $\delta(X)$ is defined to be the minimal integer $m$ so that $P_{m}(X)\geq 2$. According to Chen-Chen, one has either $1\leq \delta(X)\leq 15$ or…

We study the decay B --> K l^+ l^- for l = e,mu,tau with a softly recoiling kaon, that is, for high dilepton invariant masses sqrt{q^2} of the order of the b-quark mass. This kinematic region can be treated within an operator product…

Let $(X,\Delta)$ be a dlt log Calabi-Yau pair admitting a polarized endomorphism. We show that $(X,\Delta)$ is a finite quotient of a toric log Calabi-Yau fibration over an abelian variety. We provide an example which shows that the…

Suppose that an algebraic torus $G$ acts algebraically on a projective manifold $X$ with generically trivial stabilizers. Then the Zariski closure of the set of pairs $\{(x,y)\in X\times X\mid y=gx \text{for some}g\in G\}$ defines a nonzero…

We study relations between two log minimal models of a fixed lc pair. For any two log minimal models of an lc pair constructed with log MMP, we prove that there are small birational models of the log minimal models which can be connected by…

We study several separation axioms for $X$-top-lattices (i.e. a lattice $L$ for which a given subset $X\subseteq L\backslash \{1\}$ admits a \emph{% Zariski-like topology}). Such spaces are $T_{0}$ and usually far away from being $T_{2}.$…

Let $f$ be a morphism from a klt pair $(X, \Delta)$ to an abelian variety $A$, $m\geq1$ a rational number and $D$ a Cartier divisor on $X$ such that $D\sim_{\mathbb Q}m(K_X+\Delta)$. We prove that the sheaf $f_*\mathcal{O}_X(D)$ becomes…

We use Matsuki's decomposition for symmetric pairs $(G, H)$ of (not necessarily compact) reductive Lie groups to construct the radial parts for invariant differential operators acting on matrix-spherical functions. As an application, we…

We study the Zariski cancellation problem for Poisson algebras asking whether $A[t]\cong B[t]$ implies $A\cong B$ when $A$ and $B$ are Poisson algebras. We resolve this affirmatively in the cases when $A$ and $B$ are both connected graded…

Let $k$ be an $F$-finite field containing an infinite perfect field of positive characteristic. Let $(X, \Delta)$ be a projective log canonical pair over $k$. In this note we show that, for a semi-ample divisor $D$ on $X$, there exists an…

We reanalyse the recent version of the chiral model of weak radiative hyperon decays, proposed by Borasoy and Holstein. It is shown that predictions of the analysed model are significantly changed when one accepts the usual classification…

We consider the moduli space of log smooth pairs formed by a cubic surface and an anticanonical divisor. We describe all compactifications of this moduli space which are constructed using Geometric Invariant Theory and the anticanonical…

The linear sigma model with broken U3xU3 is compared with data on the lightest scalar and pseudoscalar mesons. When 5 of the 6 parameters are fixed by the pseudoscalar masses and decay constants one finds that, already at the tree level, a…

We calculate a number of observables related to particle-antiparticle mixing in the Littlest Higgs model with T-parity (LHT). The resulting effective Hamiltonian for Delta F=2 transitions agrees with the one of Hubisz et al., but our…

In this paper we establish existence and properties of minimal energy solutions for the weakly coupled system $$ \begin{cases} -\Delta u_i + \lambda_i u_i = \mu_i|u_i|^{Kq-2}u_i + \beta|u_i|^{q-2}u_i\prod_{j\neq i}|u_j|^q & \text{in…

We consider the decoherence free subalgebra which satisfies the minimal condition introduced by Alicki. We show the manifest form of it and relate the subalgebra with the Kraus representation. The arguments also provides a new proof for…

The available data on $|\Delta B| = |\Delta S| = 1$ decays are in good agreement with the Standard Model when permitting subleading power corrections of about 15% at large hadronic recoil. Constraining new-physics effects in…

Minimal model conjecture for a proper variety $X$ is that if $\kappa(X)\geq 0$, then $X$ has a minimal model with the abundance and if $\kappa =-\infty$, then $X$ is birationally equivalent to a variety $Y$ which has a fibration $Y \to Z$…

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…