Related papers: A Note on the Effective Non-vanishing Conjecture

We study twisted ideal sheaves of small length on an irreducible principally polarized abelian surface (T,l). Using Fourier-Mukai techniques we associate certain jumping schemes to such sheaves and completely classify such loci. We give…

We prove finiteness results for sets of varieties over number fields with good reduction outside a given finite set of places using cyclic covers. We obtain a version of the Shafarevich conjecture for weighted projective surfaces, double…

We prove the non-vanishing conjecture for lc pairs $(X,\Delta)$ when $X$ is of Calabi--Yau type.

We prove new cases of Vojta's conjectures for surfaces in the context of function fields, with truncation equal to one and providing an effective explicit description of the exceptional set. We also prove a general and explicit result…

We prove the Nonvanishing conjecture for uniruled projective log canonical pairs of dimension $n$, assuming the Nonvanishing conjecture for smooth projective varieties in dimension $n-1$. We also show that the existence of good minimal…

The goal of this paper is to make a surprising connection between several central conjectures in algebraic geometry: the Nonvanishing Conjecture, the Abundance Conjecture, and the Semiampleness Conjecture for nef line bundles on K-trivial…

We show that any pseudo-effective divisor on a normal surface decomposes uniquely into its "integral positive" part and "integral negative" part, which is an integral analog of Zariski decompositions. By using this decomposition, we give…

Let $F$ be a totally real field and $K$ a finite abelian CM extension of $F$. Using class field theory, we show that our previous result giving a strong form of the Brumer-Stark conjecture implies the minus part of the equivariant Tamagawa…

Recent literature on Weil-Petersson random hyperbolic surfaces has met a consistent obstacle: the necessity to condition the model, prohibiting certain rare geometric patterns (which we call tangles), such as short closed geodesics or…

In this paper, we give some non-vanishing results on the central values of prime twists of modular $L$-functions by imaginary quadratic fields for specific elliptic modular forms. In particular, we show that the central values of prime…

We prove a recent conjecture of Sean A. Irvine about a nonlinear recurrence, using mechanized guessing and verification. The theorem-prover Walnut plays a large role in the proof.

The paper gives the sufficient condition formulated in the syntactical form for all codescent morphisms of a variety of universal algebras satisfying the amalgamation property to be effective. This result is further used in proving that all…

In this article, we will prove the Generalized Nonvanishing Conjecture holds for threefolds with either $\kappa>0$ or $q>0$. As a result, we can prove the Iitaka conjecture $C_{n,m}$ holds for $n=7$ if the source space has non-negative…

By using non-positively curved cubings of prime alternating link exteriors, we prove that certain ideal triangulations of their complements, derived from reduced alternating diagrams, are non-degenerate, in the sense that none of the edges…

We prove that no smooth symmetric convex body $\Omega$ with at least one point of non-vanishing Gaussian curvature can admit an orthogonal basis of exponentials. (The non-symmetric case was proven by Kolountzakis). This is further evidence…

We prove that Alexandrov's conjecture relating the area and diameter of a convex surface holds for the surface of a general ellipsoid. This is a direct consequence of a more general result which estimates the deviation from the optimal…

The aim of this paper is to give an existence result for a class of one-dimensional, non-convex, non-coercive problems in the Calculus of Variations. The main tools for the proof are an existence theorem in the convex case and the closure…

We prove that exact functors between the categories of perfect complexes supported on projective schemes are of Fourier--Mukai type if the functor satisfies a condition weaker than being fully faithful. We also get generalizations of the…

Nonvanishing theorems play a central role in birational geometry, since they derive geometric consequences from numerical information and constitute a crucial step towards abundance and semiampleness problems. General nonvanishing…

This paper studies stable sheaves on abelian surfaces of Picard number one. Our main tools are semi-homogeneous sheaves and Fourier-Mukai transforms. We introduce the notion of semi-homogeneous presentation and investigate the behavior of…