Related papers: Log canonical thresholds and coregularity
We prove a base point free theorem for nef and log big divisors on log canonical surfaces.
We prove that the upper bounds for the consistency strength of certain instances of mutual stationarity considered by Liu-Shelah~\cite{MR1469093} are close to optimal. We also consider some related and, as it turns out, stronger properties.
We obtain necessary and sufficient conditions to characterize the boundedness of the composition of dyadic paraproduct operators.
We prove upper and lower bounds for leading coefficient of Kolchin dimension polynomial of systems of partial linear differential equations in codimension two.
We define log Hochschild co/homology for log schemes that behaves well for simple normal crossing pairs $(X,D)$ or toroidal singularities. We prove a Hochschild-Kostant-Rosenberg isomorphism for log smooth schemes, as well as an equivariant…
In this note we prove and disprove some chain conditions in type definable and definable groups in dependent, strongly dependent and strongly^{2} dependent theories.
This note introduces a sufficient Linear Matrix Inequality (LMI) condition for the ultimate boundedness of a class of continuous-time dynamical systems with conic uncertain/nonlinear terms.
We discuss the ascending chain condition for lengths of extremal rays. We prove that the lengths of extremal rays of $n$-dimensional $\mathbb Q$-factorial toric Fano varieties with Picard number one satisfy the ascending chain condition.
There is a proposition due to Koll\'ar 1997 on computing log canonical thresholds of certain hypersurface germs using weighted blowups, which we extend to weighted blowups with non-negative weights. Using this, we show that the log…
We prove, under suitable conditions, that there exist wall-crossing and reduction morphisms for moduli spaces of stable log pairs in all dimensions as one varies the coefficients of the divisor.
We prove the finiteness of $B$-representations of generalised log canonical pairs. As a consequence, we prove that, the (relative) abundance for a generalised semi-log canonical pair is implied by the abundance for its normalisation.…
New upper bounds on the first and the second Hilbert coefficients of a Cohen-Macaulay module over a local ring are given. Characterizations are provided for some upper bounds to be attained. The characterizations are given in terms of…
We prove Union-Closed sets conjecture.
In this paper, we prove a `cut-by-curves criterion' for an overconvergent isocrystal on a smooth variety over a field of characteristic $p>0$ to extend logarithmically to its smooth compactification whose complement is a strict normal…
Improved rates of convergence for ergodic homogeneous Markov chains are studied. In comparison to the earlier papers the setting is also generalised to the case without a unique dominated measure. Examples are provided where the new bound…
We show that every limit of log canonical thresholds of n-variable functions is also a log canonical threshold of an (n-1)-variable function.
We establish a uniform bound for the Castelnuovo-Mumford regularity of associated graded rings of parameter ideals in a generalized Cohen-Macaulay ring. As consequences, we obtain uniform bounds for the relation type and the postulation…
We prove Fujita's log spectrum conjecture. It follows from the ACC of a suitable set of pseudo-effective thresholds.
In this paper, we will prove some sufficient conditions for the solvability of groups.
In this paper, we study the singularities of a pair (X,Y) in arbitrary characteristic via jet schemes. For a smooth variety X in characteristic 0, Ein, Lazarsfeld and Mustata showed that there is a correspondence between irreducible closed…