Related papers: Extension of sections via adjoint ideals

The Kr\"otz-Stanton Extension Theorem states that the orbit map of a K-finite vector in a Hilbert representation of a linear Lie group extends to a holomorphic map to a principal fibre bundle over the complex crown domain associated to the…

We collect evidence in support of a conjecture of Griffiths, Green and Kerr on the arithmetic of extension classes of limiting mixed Hodge structures arising from semistable degenerations over a number field. After briefly summarizing how a…

We pursue the study of Ultracategories initiated by Makkai and more recently Lurie by looking at properties of Ultracategories of complete metric structures, i.e. coming from continuous model theory, instead of ultracategories of models of…

We extend a theorem of Maa, Pearl, and Bartoszynski, which links equality of interpoint distance distributions to equality of underlying multivariate distributions, beyond the restrictive class of homogeneous, translation-invariant distance…

In this paper, we develop a theory of diminished multiplier ideals on singular varieties which was introduced by Hacon, and developed by Lehmann. We prove a result regarding the termination of certain type of flips with scaling of an ample…

In this paper, we use the perspective of linear series, and in particular results following from the degeneration tools of limit linear series, to give a number of new results on existence and non-existence of branched covers of the…

Given several sequences of Hermitian holomorphic line bundles $\{(L_{kp}, h_{kp})\}_{p=1}^{\infty}$, we establish the distribution of common zeros of random holomorphic sections of $L_{kp}$ with respect to singular measures. We also study…

Several authors have recently constructed characteristic classes for classes of infinite rank vector bundles appearing in topology and physics. These include the tangent bundle to the space of maps between closed manifolds, the infinite…

This paper deals with codimension one (may be singular) foliations on compact K\"alher manifolds whose conormal bundle is assumed to be pseudo-effective. Using currents with minimal singularities, we show that one can endow the space of…

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 give a complete proof of a propagation theorem of multiplicity-free property from fibers to spaces of global sections for holomorphic vector bundles. The propagation theorem is formalised in three ways, aiming for producing various…

This paper demonstrates the existence of $\mathbb{Q}$-complements for algebraically integrable log-Fano foliations on klt ambient varieties. Additionally, we investigate properties of algebraically integrable Fano foliations such as a…

In this paper we study some properties of quadrilaterals concerning concurrence of lines under few to none restrictive conditions, and obtain an extension of a transversal theorem from triangles to quadrilaterals.

The technique of symmetric extensions is derived from forcing and it is one of the most important tools for studying models without the Axiom of Choice. Despite being incredibly successful since the 1960s, our understanding of the technique…

We introduce the notion of free decomposition spaces: they are simplicial spaces freely generated by their inert maps. We show that left Kan extension along the inclusion $j \colon \Delta_{\operatorname{inert}} \to \Delta$ takes general…

In this paper, we extend the fundamental theorem for submanifolds to general ambient spaces by viewing it as a higher codimensional Cartan-Ambrose-Hicks theorem. The key ingredient in obtaining this is a generalization of development of…

Using representations of vertex operator algebras, we describe the line bundles on a wide range of contractions of $\overline{\rm{M}}_{0,n}$, the moduli space of stable $n$-pointed rational curves, by proving a stronger version of the…

Among Thurston maps (orientation-preserving, postcritically finite branched coverings of the 2-sphere to itself), those that arise as subdivision maps of a finite subdivision rule form a special family. For such maps, we investigate…

For $\mathbb Q$-factorial klt algebraically integrable adjoint foliated structures, we prove the cone theorem, the contraction theorem, and the existence of flips. Therefore, we deduce the existence of the minimal model program for such…

We provide a framework to triangulate subfactor categories of additive categories with additive endofunctors. It is proved that such a framework is sufficiently flexible to cover many instances in algebra and geometry where abelian, exact…