相关论文: Fano's inequality is also false for three-dimensio…
We classify Q-factorial Gorenstein Fano non-degenerate complete intersection threefolds in fake weighted projective spaces.
A class of three-dimensional models which satisfy supersymmetric intertwining relations with the simplest - oscillator-like - variant of shape invariance is constructed. It is proved that the models are not amenable to conventional…
In this paper, a generalization of Ramanujan's cubic transformation, in the form of an inequality, is proved for zero-balanced Gaussian hypergeometric function $F(a,b;a+b;x)$, $a,b>0$.
Some sharp quadratic reverses for the generalised triangle inequality in inner product spaces and applications are given.
This is a survey on the Fano schemes of linear spaces, conics, rational curves, and curves of higher genera in smooth projective hypersurfaces, complete intersections, Fano threefolds, etc.
We prove that a quasi-smooth Fano threefold hypersurface is birationally rigid if and only if it has Fano index one.
It is shown that a smooth global deformation of quartic double solids, i.e. double covers of $\mathbb P^3$ branched along smooth quartics, is again a quartic double solid without assuming the projectivity of the global deformation. The…
We show that a nef and big line bundle whose adjoint bundle has non-zero global sections on a nonsingular toric weak Fano 3-fold is normally generated. As a consequence, we see that all ample line bundles on a nonsingular toric weak Fano…
We classify three-dimensional nodal Fano varieties that are double covers of smooth quadrics branched over intersections with quartics acted on by finite simple non-abelian groups, and study their rationality.
We compute global log canonical thresholds, or equivalently alpha invariants, of birationally rigid orbifold Fano threefolds embedded in weighted projective spaces as codimension two or three. As an important application, we prove that most…
We show that mixed-characteristic and equi-characteristic small deformations of 3-dimensional canonical (resp. terminal) singularities with perfect residue field of characteristic $p>5$ are canonical (resp. terminal). We discuss…
We obtain a sufficient condition for a Fano threefold with terminal singularities to have a conic bundle structure.
Our earlier proof of mirror formulas for genus 0 Gromov -- Witten invariants of Fano and Calabi -- Yau toric complete intersections is illustrated in the example of quintic 3-folds.
We develop the quadratic technique of proving birational rigidity of Fano-Mori fibre spaces over a higher-dimensional base. As an application, we prove birational rigidity of generic fibrations into Fano double spaces of dimension…
We prove that the deformations of a smooth complex Fano threefold X with Picard number 1, index 1, and degree 10, are unobstructed. The differential of the period map has two-dimensional kernel. We construct two two-dimensional components…
In this paper we study smooth toric Fano varieties using primitive relations and toric Mori theory. We show that for any irreducible invariant divisor D in a toric Fano variety X, we have $0\leq\rho_X-\rho_D\leq 3$, for the difference of…
In this paper a large class of Fano double quadrics and cubics are shown to be factorial and birationally superrigid, in particular they admit no non-trivial structure of a fibration with rationally connected fibres and are therefore…
We classify special self-birational transformations of the smooth quadric threefold and fourfold, $Q^3$ and $Q^4$. It turns out that there is only one such example in each dimension. In the case of $Q^3$, it is given by the linear system of…
We prove divisorial canonicity of Fano hypersurfaces and double spaces of general position with elementary singularities.
We study unirationality of actions of finite groups on Fano threefolds.