Related papers: On Fujita's spectrum conjecture

We calculate a class of polarized fermion string scattering amplitudes (PFSSA) at arbitrary mass levels. We discover that, in the hard scattering limit, the functional forms of the non-vanishing PFSSA at each fixed mass level are…

Consider a smooth, projective family of canonically polarized varieties over a smooth, quasi-projective base manifold Y, all defined over the complex numbers. It has been conjectured that the family is necessarily isotrivial if Y is special…

We prove Shokurov's index conjecture for quotient singularities.

In this paper, we show how to prove the basepoint-freeness for linear systems on irregular varieties inductively. For instance, we prove that Fujita's conjecture holds for irregular varieties of dimension $\mathnormal{n}$ with a nef…

We study the shifted convolution sums associated to completely multiplicative functions taking values in $\{\pm 1\}$ and give combinatorical proofs of two recent results in the direction of Chowla's conjecture. We also determine the…

We prove tight estimates for averages of the twisted Hooley $\Delta$-function over arbitrary number fields.

We prove that a conjecture of Fujita on the semi-ampleness is true in the case of rank one direct summand, though it is wrong in higher rank case by Catanese and Dettweiler.

In 2017, Garunk\v{s}tis, Laurin\v{c}ikas and Macaitien\.{e} proved the discrete universality theorem for the Riemann zeta-function sifted by the nontrivial zeros of the Riemann zeta-function. This discrete universality has been extended in…

We prove that Generalized Mukai Conjecture holds for Fano manifolds $X$ of pseudoindex $i_X \ge (\dim X +3)/3$. We also give different proofs of the conjecture for Fano fourfolds and fivefolds.

We obtain new partial results supporting the spectral set conjecture in dimension 1.

Let k be an infinite perfect field. We provide a general criterion for a spectrum in the stable homotopy category over k to be effective, i.e. to be in the localizing subcategory generated by the suspension spectra of smooth schemes. As a…

We provide a proof of a variant of the Landau-Siegel Zeros conjecture.

Multifractal analysis of stochastic processes deals with the fine scale properties of the sample paths and seeks for some global scaling property that would enable extracting the so-called spectrum of singularities. In this paper we…

We prove a Fourier restriction estimate under the assumption that certain convolution power of the measure admits an $r$-integrable density.

I propose a few increasingly stronger "superadditivity" conjectures regarding the behavior of Kodaira dimension under morphisms of smooth quasi-projective complex varieties.

This paper proposes a Fujita-type freeness conjecture for semi-log canonical pairs. We prove it for curves and surfaces by using the theory of quasi-log schemes and give some effective very ampleness results for stable surfaces and semi-log…

Recently, the author and Yamamoto invented a new proof of the duality for multiple zeta values. The technique is applicable in other series identities. In this article, we exhibit such proofs for some series identities.

We prove the main conjecture of arXiv:2102.13459 for integral coefficients in the case of tori and prove that it is t-exact. Along the way we prove that the spectral action as constructed in that manuscript is compatible with the action of…

We prove some results which give sufficient conditions so that pointwise approximation of negative plurisubharmonic functions on complex varieties by continuous plurisubharmonic ones is possible.

We describe the Dirichlet spectrum structure for the Fichera layers and crosses in any dimension $n\ge3$. Also the application of the obtained results to the classical Brownian exit times problem in these domains.