Related papers: An explicit bound for complements on toric varieti…
We give explicit upper bounds for the coefficients of arbitrary weight $k$, level 2 cusp forms, making Deligne's well-known $O(n^{\frac{k-1}{2}+\epsilon})$ bound precise. We also derive asymptotic formulas and explicit upper bounds for the…
We give a sharp upper bound for the entries of the representations of a rational number as a sum of Egyptian fractions.
Let A be an abelian variety defined over a number field K, and consider the canonical height function attached to a symmetric ample line bundle L on A. We prove that there is a positive lower bound C (depending on A, K, and L) for the…
We give a structure theorem for n-dimensional smooth toric Fano varieties whose associated polytope has "many" pairs of centrally symmetric vertices.
Tur\'an number is one of primary topics in the combinatorics of finite sets,in this paper, we will present a new upper bound for Tur\'an number.
We prove the existence of K\"ahler-Ricci solitons on toric Fano orbifolds, hence extend the the theorem of Wang and Zhu [WZ] to the orbifold case.
We completely classify the Q-factorial terminal toric Fano three-folds such that the sum of the squared torus invariant prime divisors is non-negative.
The aim of this paper is to clarify and generalize techniques of works alg-geom/9711024 (see also math.AG/9810097 and math.AG/9901004). Roughly speaking, we prove that for local Fano contractions the existence of complements can be reduced…
We give a formula for the specialization of the Fourier-Mukai transform on a semi-abelian variety of torus rank 1.
We classify smooth toric Fano varieties of dimension $n\geq 3$ containing a toric divisor isomorphic to $\PP^{n-1}$. As a consequence of this classification, we show that any smooth complete toric variety $X$ of dimension $n\geq 3$ with a…
We show that the Picard rank is constant in families of Fano varieties (in arbitrary characteristic) and we moreover investigate the constancy of the index.
An upper bound of composition series of groups of finite order is obtained. The bound is a nontrivial bound and so far best possible.
We introduce birational strong complete regularity and strong complete regularity, two numerical invariants for pairs of (relative) Fano type. They are defined using variants of qdlt Fano type models and the dimension of the dual complex of…
For $n\geq 4$, let $X$ be a complex smooth Fano $n$-fold whose minimal anticanonical degree of non-free rational curves on $X$ is at least $n-2$. We classify extremal contractions of such varieties. As an application, we obtain a…
We consider subtorus actions on complex toric varieties. A natural candidate for a categorical quotient of such an action is the so-called toric quotient, a universal object constructed in the toric category. We prove that if the toric…
In this article, we consider the maximal value of the Thurston--Bennequin invariant of Legendrian knots which topologically represent a fixed knot type in the standard contact 3-space and we prove a formula of the value under the connected…
We show that the optimal upper bound for the anticanonical degrees of non-Gorenstein $\mathbb{Q}$-factorial canonical Fano threefolds with Picard number one is 200/3.
We give an explicit upper bound for the degree of a tropical basis of a homogeneous polynomial ideal. As an application f-vectors of tropical varieties are discussed. Various examples illustrate differences between Gr\"obner and tropical…
Consider a smooth log Fano variety over the function field of a curve. Suppose that the boundary has positive normal bundle. Choose an integral model over the curve. Then integral points are Zariski dense, after removing an explicit finite…
In this paper we obtain further improvement of index bounds for character sums of polynomials over finite fields. We present some examples, which show that our new bound is an improved bound compared to both the Weil bound and the index…