Related papers: Log canonical threshold, Segre classes, and polyga…

We present a method to compute the degrees of the Segre classes of a subscheme of complex projective space. The method is based on generic residuation and intersection theory. It has been implemented using the software system Macaulay2.

We present a probabilistic algorithm to test if a homogeneous polynomial ideal $I$ defining a scheme $X$ in $\mathbb{P}^n$ is radical using Segre classes and other geometric notions from intersection theory. Its worst case complexity…

Let X be a smooth variety over a field of positive characteristic, and let E be an overconvergent isocrystal on X. We establish a criterion for the existence of a "canonical logarithmic extension" of E to a good compactification of X. In…

Let p be a trigonometric polynomial, nonnegative on the unit circle $\mathbb{T}$. We say that a measure $\sigma$ on $\mathbb{T}$ belongs to the polynomial Szego class, if $d\sigma=sigma'_{ac}d\theta+d\sigma_s$, $\sigma_s$ is singular, and…

In this article, we will characterize the multiplier ideal sheaves with weights of log canonical threshold one by restricting the weights to complex regular surface.

We propose a new realization, using Harish-Chandra bimodules, of the Serre functor for the BGG category $\mathcal{O}$ associated to a semi-simple complex finite dimensional Lie algebra. We further show that our realization carries over to…

The monoidal category of Soergel bimodules can be thought of as a categorification of the Hecke algebra of a finite Weyl group. We present this category, when the Weyl group is the symmetric group, in the language of planar diagrams with…

We show that log canonical thresholds of fixed dimension are standardized. More precisely, we show that any sequence of log canonical thresholds in fixed dimension $d$ accumulates in a way which is i) either similar to how standard and…

We prove that there is no g for which the canonical embedding of a general curve of genus g lies on the Segre embedding of any product of three or more projective spaces.

The aim of the work is to construct new polynomial systems, which are solutions to certain functional equations which generalize the second-order differential equations satisfied by the so called classical orthogonal polynomial families of…

This paper is about the logarithmic limit sets of real semi-algebraic sets, and, more generally, about the logarithmic limit sets of sets definable in an o-minimal, polynomially bounded structure. We prove that most of the properties of the…

We provide a categorical interpretation of a well-known identity from linear algebra as an isomorphism of certain functors between triangulated categories arising from finite dimensional algebras. As a consequence, we deduce that the Serre…

We propose a variation of the notion of Segre class, by forcing a naive `inclusion-exclusion' principle to hold. The resulting class is computationally tractable, and is closely related to Chern-Schwartz-MacPherson classes. We deduce…

We use intersection theory, degeneration techniques and jet schemes to study log canonical thresholds. Our first result gives a lower bound for the log canonical threshold of a pair in terms of the log canonical threshold of the image by a…

In this paper, we show the log canonical threshold values of the surfaces which has du Val type singularities.These surfaces can be interpreted as statistical or machine learning models. The results of $A_n, D_n, E_6, E_7$ and $E_8$ are…

The Segre determinant is a polynomial which encodes the condition for points to lie on a bilinear hypersurface in the product of projective spaces. We study Segre determinants and compute them in various coordinate systems. We show that the…

The log canonical thresholds of irreducible quasi-ordinary hypersurface singularities are computed, using an explicit list of pole candidates for the motivic zeta function found by the last two authors.

We compute the multidegrees and the Segre numbers of general determinantal Cremona transformations, with generically reduced base scheme, by specializing to the standard Cremona transformation and computing its Segre class via mixed volumes…

It is well-known that the category of Kleisli algebras for a monoidal monad carries a canonical monoidal structure. We define the notion of a commutative graded monad and present a strictly two-categorical proof that Kleisli algebras for…

We define and study LNL polycategories, which abstract the judgmental structure of classical linear logic with exponentials. Many existing structures can be represented as LNL polycategories, including LNL adjunctions, linear exponential…