相关论文: Fano's inequality is a mistake

The aim of this paper is to analyze the weighted KyFan inequality proposed in [11]. A number of numerical simulations involving the exponential weighted function is given. We show that in several cases and types of examples one can imply an…

In statistical inference problems, we wish to obtain lower bounds on the minimax risk, that is to bound the performance of any possible estimator. A standard technique to obtain risk lower bounds involves the use of Fano's inequality. In an…

In this paper we prove transference inequalities for regular and uniform Diophantine exponents in the weighted setting. Our results generalize the corresponding inequalities that exist in the `non-weighted' case.

We analize the semistable degeneration of the Fano surface F when the cubic threefold becomes the Segre primal. This gives an explicit topological decomposition for F. The decomposition is used to decide that the Fano surface is not an an…

There exists a certain argument that in even dimensions, scale invariant quantum field theories are conformal invariant. We may try to extend the argument in $2n + \epsilon$ dimensions, but the naive extension has a small loophole, which…

In brane world scenarios the Friedmann equation is modified, resulting in an increased expansion at early times. This has important effects on cosmological phase transitions which we investigate, elucidating significant differences to the…

We generalize the definition of alpha invariant to arbitrary codimension. We also give a lower bound of these alpha invariants for K-semistable Q-Fano varieties and show that we can characterize projective spaces among all K-semistable Fano…

Form invariance transformations can be used for constructing phantom cosmologies starting with conventional cosmological models. In this work we reconsider the scalar field case and extend the discussion to fermionic fields, where the…

We construct exceptional Fano varieties with the smallest known minimal log discrepancies in all dimensions. These varieties are well-formed hypersurfaces in weighted projective space. Their minimal log discrepancies decay doubly…

The purpose of this paper is to compute the degree of irrationality of hypersurfaces of sufficiently high degree in various Fano varieties: quadrics, Grassmannians, products of projective space, cubic threefolds, cubic fourfolds, and…

Within an axiomatic framework for three-dimensional projective space based on lines alone, we explore the Fano axiom of harmonicity according to which the diagonal lines of a complete quadrilateral are not concurrent.

An argument is provided for the equality case of the high dimensional Bonnesen inequality for sections. The known equality case of the Bonnesen inequality for projections is presented as a consequence.

We study the quasi-projective variety Bir_d of plane Cremona transformations defined by three polynomials of fixed degree d and its subvariety Bir_d^o where the three polynomials have no common factor. We compute their dimension and the…

We classify complex projective manifolds $X$ for which there exists a point $a$ such that the blow-up of $X$ at $a$ is Fano.

In 1940, Luis Santal\'o proved a Helly-type theorem for line transversals to boxes in R^d. An analysis of his proof reveals a convexity structure for ascending lines in R^d that is isomorphic to the ordinary notion of convexity in a convex…

In [Decompositions and statistics for \beta(1,0)-trees and nonseparable permutations, Advances Appl. Math. 42 (2009) 313--328] we introduced an involution, h, on \beta(1,0)-trees. We neglected, however, to prove that h indeed is an…

We describe the set of Mori structures for a Fano 3-fold of index 2 and degree 1 (the double cone over the Veronese surface). In partiular, it is proved that such a Fano variety is not rational, the group of birational automorphisms…

An alternative interpretation of the conformal transformations of the metric is discussed according to which the latter can be viewed as a mapping among Riemannian and Weyl-integrable spaces. A novel aspect of the conformal transformation's…

In recent years new types of coordinate transformations have appeared in cosmology on top of the standard gauge transformations, such as the dilatations and special conformal transformations, or the ones leading to (conformal) Fermi…

The Majorana transformation makes it possible to reduce the Thomas-Fermi equation to a first-order differential equation. This reduction is possible due to the special scaling property of the Thomas-Fermi equation under homology…