Related papers: Remarks on log pluricanonical representations
We prove that there are only finitely many arithmetic Kleinian maximal reflection groups.
We state a conjecture on the reduction modulo the defining characteristic of a unipotent representation of a finite reductive group.
We show the existence of prime divisors computing minimal log discrepancies in positive characteristic except for a special case. Moreover we prove the lower semicontinuity of minimal log discrepancies for smooth varieties in positive…
Let $K$ be an unramified $p$-adic local field and let $W$ be the ring of integers of $K$. Let $(X,S)/W$ be a smooth proper scheme together with a normal crossings divisor. We show that there are only finitely many log crystalline $\mathbb…
A plurisubharmonic weight is log canonical if it is at the critical point of turning non-integrable. Given a log canonical plurisubharmonic weight, we show that locally there always exists a log canonical `holomorphic' weight having the…
Under the assumption of the minimal model theory for projective klt pairs of dimension $n$, we establish the minimal model theory for lc pairs $(X/Z,\Delta)$ such that the log canonical divisor is relatively log abundant and its restriction…
We give a topological bound on the number of minimal models of a class of three dimensional log smooth pairs of general type.
We prove the existence of pl-flips.
We compare the minimal model of a log canonical pair with the minimal model of its reduced boundary. These results are then used to study the existence of the minimal model of a semi-log-canonical pair using its normalization.
We give a description of the minimal exponent of a hypersurface using higher direct images of suitably twisted sheaves of log forms on a log resolution.
It is discussed how a limiting procedure of (super)conformal field theories may result in logarithmic (super)conformal field theories. The construction is illustrated by logarithmic limits of (unitary) minimal models in conformal field…
We prove that, up to adding a complement, every modular representation of a finite group admits a finite resolution by permutation modules.
We give parameterizations of the irreducible representations of finite groups of Lie type in their defining characteristic.
We treat two different topics on the log minimal model program, especially for four-dimensional log canonical pairs. (a) Finite generation of the log canonical ring in dimension four. (b) Abundance theorem for irregular fourfolds. We obtain…
We determine, complementing a paper by Marcel Morales, the log-pluricanonical forms on a nondegenerate hypersurface. This description shows that they are extendable to 1-parameter deformations. For an equisingular deformation we thus obtain…
We prove a result that enables us to calculate the rational homotopy of a wide class of spaces by the theory of minimal models.
We consider the dimensions of finite type of representations of a partially ordered set, i.e. such that there is only finitely many isomorphism classes of representations of this dimension. We give a criterion for a dimension to be of…
We prove that the equational complexity function for the variety of representable relation algebras is bounded below by a log-log function.
We prove two theorems on the locally finite decompositions of the cones of divisors by the cones which correspond to canonical and minimal models. We introduce the concept of the numerical linear systems in order to simplify the argument on…
We investigate the variation of log canonical thresholds in (graded) linear systems. For toric log Fano varieties, we give a sharp lower bound for log canonical thresholds of the anticanonical members in terms of the global minimal log…