Related papers: On Fujita's spectrum conjecture

We prove Fujita's log spectrum conjecture. It follows from the ACC of a suitable set of pseudo-effective thresholds.

We show Fujita's spectrum conjecture for $\epsilon$-log canonical pairs and Fujita's log spectrum conjecture for log canonical pairs. Then, we generalize the pseudo-effective threshold of a single divisor to multiple divisors and establish…

We characterize a $k$-th accumulation point of pseudo-effective thresholds of $n$-dimensional varieties as certain invariant associates to a numerically trivial pair of an $(n-k)$-dimensional variety. This characterization is applied…

We show that $k$-th iterated accumulation points of pseudo-effective thresholds of $n$-dimensional varieties are bounded by $n-k+1$.

We prove Fujita's freeness conjecture for Gorenstein complexity-one $T$-varieties with rational singularities.

We prove a version of Fujita's Conjecture in arbitrary characteristic, generalizing results of K.E. Smith. Our methods use the Frobenius morphism, but avoid tight closure theory. We also obtain versions of Fujita's Conjecture for coherent…

We present a self-contained combinatorial approach to Fujita's conjectures in the toric case. Our main new result is a generalization of Fujita's very ampleness conjecture for toric varieties with arbitrary singularities. In an appendix, we…

Fujita's conjecture is known to be false in positive characteristic. We conjecture and give an approach to a new variant of Fujita's conjecture for the basepoint-freeness, very ampleness, and jet ampleness of linear systems of the form…

In this paper, we examine an analogue of the recently solved spectrum conjecture by Fujita in the setting of Fine polyhedral adjunction theory. We present computational results for lower-dimensional polytopes, which lead to a complete…

We consider Fujita's freeness conjecture in a relative setting and prove a criterion by proving a correct Q-divisor version of the Kollar vanishing theorem.

We state and prove a function field analogue of Furusho for multiple zeta values.

We prove under some assumptions that the Tate conjecture holds for products of Fermat varieties of different degrees.

Given a morphism between complex projective varieties, we make several conjectures on the relations between the set of pseudo-effective (co)homology classes which are annihilated by pushforward and the set of classes of varieties contracted…

We first prove Vojta's abc conjecture over function fields for Campana points on projective toric varieties with high multiplicity along the boundary. As a consequence, we obtain a version of Campana's conjecture on finite coverings of…

Let X be a smooth complex projective variety of dimension n. We prove bounds on Fujita's basepoint freeness conjecture that grow as nloglog(n).

We prove a mixed joint discrete universality theorem for a Matsumoto zeta-function $\varphi(s)$ (belonging to the Steuding subclass) and a periodic Hurwitz zeta-function $\zeta(s,\alpha;{\mathfrak{B}})$. For this purpose, certain…

In this paper we show that the spectrum of the Q-codegree of a d-dimensional lattice polytope is finite above any positive threshold in the class of lattice polytopes with \alpha-canonical normal fan for any fixed \alpha>0. For \alpha=1/r…

Motivated by Lang-Vojta's conjectures on hyperbolic varieties, we prove a new version of the Shafarevich conjecture in which we establish the finiteness of pointed families of polarized varieties. We then give an arithmetic application to…

In this paper, we show that Fujita's basepoint-freeness conjecture for projective quasi-log canonical singularities holds true in dimension three. Immediately, we prove Fujita-type basepoint-freeness for projective semi-log canonical…

We give new estimates of lengths of extremal rays of birational type for toric varieties. We can see that our new estimates are the best by constructing some examples explicitly. As applications, we discuss the nefness and…