Related papers: Zariski decompositions of numerical cycle classes
We first prove some basic properties of Okounkov bodies, and give a characterization of Nakayama and positive volume subvarieties of a pseudoeffective divisor in terms of Okounkov bodies. Next, we show that each valuative and limiting…
We formalize the main approach for showing Zariski descent-type statements for strong generation of triangulated categories associated to algebro-geometric objects. This recovers various known statements in the literature. As applications…
We study the concordance and bordism of decompositions associated with defining sequences and we relate them to some invariants of toroidal decompositions and to the cobordism of homology manifolds. These decompositions are often wild…
The article contains a survey of our results on weakly commensurable arithmetic and general Zariski-dense subgroups, length-commensurable and isospectral locally symmetric spaces and of related problems in the theory of semi-simple agebraic…
In this article, we study the Zariski closure of modular points in the two-dimensional universal deformation space when the residual Galois representation is reducible. Unlike the previous approaches in the residually irreducible case from…
The prime geodesic theorem for cycles in Bruhat-Tits buildings is applied to unit groups of division algebras to derive new asymptotic assertion on class numbers of orders in imaginary quadratic fields.
We extend a holomorphic projection argument of our earlier work to prove a novel divisibility result for non-holomorphic congruences of Hurwitz class numbers. This result allows us to establish Ramanujan-type congruences for Hurwitz class…
In this paper we introduce new class of multiplicative interactions of the $\zeta$-oscillating systems generated by a subset of power functions. The main result obtained expresses an analogue of prime decomposition (without the property of…
The constructions of the virtual Euler (or moduli) cycles and their properties are explained and developed systematically in the general abstract settings.
Quasi-cyclic codes form an important class of algebraic codes that includes cyclic codes as a special subclass. This chapter focuses on the algebraic structure of quasi-cyclic codes, first. Based on these structural properties, some…
The combinatorial description via ribbon graphs of the moduli space of Riemann surfaces makes it possible to define combinatorial cycles in a natural way. Witten and Kontsevich first conjectured that these classes are polynomials in the…
Decomposition algebras and axial decomposition algebras are classes of commutative nonassociative algebras which are generalizations of axial algebras. The classes decomposition algebras, axial decomposition al;gebras and non-primitive…
Formulas about the side lengths, diagonal lengths or radius of the circumcircle of a cyclic polygon in Euclidean geometry, hyperbolic geometry or spherical geometry can be unified.
We prove a new symplectic analogue of Kashiwara's Equivalence from D-module theory. As a consequence, we establish a structure theory for module categories over deformation quantizations that mirrors, at a higher categorical level, the…
In this paper, we study the geometry of two-torsion points of elliptic curves in order to distinguish the embedded topology of reducible plane curves consisting of a smooth cubic and its tangent lines. As a result, we obtain a new family of…
We investigate the relation between Klingen's decomposition of the space of Siegel modular forms and Dulinski's analogous decomposition of the space of Jacobi forms.
The purpose of this paper is to provide a new account of multiplicity for finite morphisms between smooth projective varieties. Traditionally, this has been defined using commutative algebra in terms of the length of integral ring…
We give an example of a one dimensional foliation $\cal F$ of degree two in a Zariski open set of a four dimensional weighted projective space which has only an enumerable set of algebraic leaves. These are defined over rational numbers and…
If $X$ is a rational surface without nonzero holomorphic vector field and $f$ is an automorphism of $X$, we study in several examples the Zariski tangent space of the local deformation space of the pair $(X, f)$.
We study the transfer of (co)silting objects in derived categories of module categories via the extension functors induced by a morphism of commutative rings. It is proved that the extension functors preserve (co)silting objects of…