Related papers: Log Canonical Thresholds for Plane Curves in Arbit…
We adopt a statistical point of view on the conjecture of Lang which predicts a lower bound for the canonical height of non-torsion rational points on elliptic curves defined over $\mathbb{Q}$. More specifically, we prove that among the…
We study the limits of PGL(3) translates of an arbitrary plane curve, giving a description of all possible limits of a given curve and computing the multiplicities of corresponding components in the normal cone to the base scheme of a…
The main aim of the note is to provide an upper-bound for the characteristic number of conic-line arrangements with ordinary singularities in the complex projective plane.
We derive recursive equations for the characteristic numbers of rational nodal plane curves with at most one cusp, subject to point conditions, tangent conditions and flag conditions, developing techniques akin to quantum cohomology on a…
A conditional bound is given for the average analytic rank of elliptic curves over an arbitrary number field. In particular, under the assumptions that all elliptic curves over a number field $K$ are modular and have $L$-functions which…
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…
We discuss the relative log minimal model theory for log surfaces in the analytic setting. More precisely, we show that the minimal model program, the abundance theorem, and the finite generation of log canonical rings hold for log pairs of…
We prove that the log canonical threshold of the base ideal of a complete linear system on a complex abelian variety is $\ge 1$, and equality holds if and only if the base locus has divisorial components. Consequently the same assertions…
The present paper is concerned with differential forms on log canonical varieties. It is shown that any p-form defined on the smooth locus of a variety with canonical or klt singularities extends regularly to any resolution of…
We study logarithmic jet schemes of a log scheme and generalize a theorem of M. Mustata from the case of ordinary jet schemes to the logarithmic case. If X is a normal local complete intersection log variety, then X has canonical…
We prove a central limit theorem for the logarithm of the characteristic polynomial of random Jacobi matrices. Our results cover the G$\beta$E models for $\beta>0$.
The characteristic numbers of smooth plane quartics are computed using intersection theory on a component of the moduli space of stable maps. This completes the verification of Zeuthen's prediction of characteristic numbers of smooth plane…
In this paper, we consider a problem of Lang about finiteness of torsion points on plane rational curves over $\mathbb C$, and prove some results towards a matrix analogue of this problem.
In this paper, we consider a class of plane curves called log-aesthetic curves and their generalization which are used in computer aided geometric design. We consider these curves in the framework of the similarity geometry and characterize…
Hassett and Keel predicted that there is a descending sequence of critical $\alpha$ values where the log canonical model for the moduli space of stable curves with respect to $\alpha \delta$ changes. We derive a conjectural formula for the…
In this paper we give a formal expression to the limits of dual plane curves by using the method introduced by Katz. As an application, we give a formula to compute the vertices of $C(0)$ a plane curve in $C(t)$ a one-parameter family of…
We classify all possible limits of families of translates of a fixed, arbitrary complex plane curve. We do this by giving a set-theoretic description of the projective normal cone (PNC) of the base scheme of a natural rational map,…
The central limit theorem for convex bodies says that with high probability the marginal of an isotropic log-concave distribution along a random direction is close to a Gaussian, with the quantitative difference determined asymptotically by…
The General Curve Lemma is a tool of Infinite-Dimensional Analysis, which enables refined studies of differentiability properties of mappings between real locally convex spaces. In this article, we generalize the General Curve Lemma in two…
The log-aesthetic curve has a significant factor in the field of aesthetic design to meet the high industrial requirements. It has much exceptional property and a large number of research papers are published, since its introduction. It can…