Related papers: On inversion of adjunction

We propose a variant of the effective adjunction conjecture for lc-trivial fibrations. This variant is suitable for inductions and can be used to treat real coefficients.

This note analyzes in terms of categorial proof theory some standard assumptions about negation in the absence of any other connective. It is shown that the assumptions for an involutive negation, like classical negation, make a kind of…

This is a first instalment of much larger work about relations between birational geometry and moduli of triples. The extraction of work is mainly related to Theorem 6. It is a weak version of Kawamata's Conjecture 1 and an important…

We give counterexamples to Okounkov's log-concavity conjecture for Littlewood-Richardson coefficients.

For every adjunction of stable $\infty$-categories -- or more generally, in any locally stable $(\infty,2)$-category -- we give a simple procedure for inverting the twist and cotwist functors associated to this adjunction. As a consequence,…

By suitable examples we illustrate an algorithm for composition of inverse problems.

We show that some properties of log canonical centers of a log canonical pair (X,D) also hold for certain subvarieties that are close to being a log canonical center. As a consequence, we obtain that if one works with deformations of pairs…

In this article we give two independent proofs of the positive characteristic analog of the log terminal inversion of adjunction. We show that for a pair $(X, S+B)$ in characteristic $p>0$, if $(S^n, B_{S^n})$ is strongly $F$-regular, then…

We prove an inverse relation and a family of convolution formulas involving partial Bell polynomials. Known and some presumably new combinatorial identities of convolution type are discussed. Our approach relies on an interesting…

We establish new results on weighted $L^2$ extension of holomorphic top forms with values in a holomorphic line bundle, from a smooth hypersurface cut out by a holomorphic function. The weights we use are determined by certain functions…

We prove new entropy inequalities for log concave and s-concave functions that strengthen and generalize recently established reverse log Sobolev and Poincare inequalities for such functions. This leads naturally to the concept of…

We discuss adjunction formulas for fiber spaces and embeddings, extending the known results along the lines of the Adjunction Conjecture, independently proposed by Y. Kawamata and V.V. Shokurov. As an application, we simplify Koll\'ar's…

We prove the finiteness of relative log pluricanonical representations in the complex analytic setting. As an application, we discuss the abundance conjecture for semi-log canonical pairs within this framework. Furthermore, we establish the…

We categorify the adjunction between locales and topological spaces, this amounts to an adjunction between (generalized) bounded ionads and topoi. We show that the adjunction is idempotent. We relate this adjunction to the Scott adjunction,…

In this work we present an analogue of the inverse scattering for Canonical systems using theory of vessels and associated to them completely integrable systems. Analytic coefficients fits into this setting, significantly expanding the…

We investigate certain adjunctions in derived categories of equivariant spectra, including a right adjoint to fixed points, a right adjoint to pullback by an isometry of universes, and a chain of two right adjoints to geometric fixed…

We present a generalization of the multiplier ideal version of inversion of adjunction, often known as the restriction theorem, to centers of arbitrary codimension. We approach inversion of adjunction from the subadjunction point of view.…

We investigate several categories related to transition structures, using a mixture of algebraic and topological methods. We show how two such categories are connected by a contravariant adjunction. This is the most detailed of a family of…

We generalize the rationality theorem of the accumulation points of log canonical thresholds which was proved by Hacon, M\textsuperscript{c}Kernan, and Xu. Further, we apply the rationality to the ACC problem on the minimal log…

In the context of infinity categories, we rethink the notion of derived functor in terms of correspondences. This is especially convenient for the description of a passage from an adjoint pair (F,G) of functors to a derived adjoint pair…