Related papers: Elliptic structures on weighted three-dimensional …

We study birational transformations into elliptic fibrations and birational automorphisms of quasismooth anticanonically embedded weighted Fano 3-fold hypersurfaces having terminal singularities classified by A.R. Iano-Fletcher, J. Johnson,…

A complete classification is presented of elliptic and K3 fibrations birational to certain mildly singular complex Fano 3-folds. Detailed proofs are given for one example case, namely that of a general hypersurface X of degree 30 in…

Let $V_1$ be the Fano threefold given as a hypersurface of degree 6 in $P(1,1,1,2,3)$ (over a number field $K$). Then there exists a finite extension $K'/K$ such that the set of $K'$-rational points of $X$ is Zariski dense.

We classify, up to automorphisms, the elliptic fibrations on the singular K3 surface $X$ whose transcendental lattice is isometric to $\langle 6\rangle\oplus \langle 2\rangle$.

We show that the degrees of rational endomorphisms of very general complex Fano and Calabi-Yau hypersurfaces satisfy certain congruence conditions by specializing to characteristic p. As a corollary we show that very general n-dimensional…

We classify four-dimensional quasismooth weighted hypersurfaces with small canonical class, and verify a conjecture of Johnson and Kollar on infinite series of quasismooth hypersurfaces with anticanonical hyperplane section in the case of…

It is proved that a general Fano hypersurface of index 1 (in the projective space) with isolated singularities of general position is birationally rigid. Therefore it cannot be fibered into uniruled varieties of a smaller dimension by a…

It is shown that hypersurfaces of degree $M$ in ${\mathbb P}^M$, $M\geqslant 5$, with at most quadratic singularities of rank at least 3, satisfying certain conditions of general position, are birationally superrigid Fano varieties and the…

We study degree of irrationality of quasismooth anticanonically embedded weighted Fano 3-fold hypersurfaces that have terminal singularities.

We classify elliptic fibrations birational to a nonsingular, minimal cubic surface over a field of characteristic zero. Our proof is adapted to provide computational techniques for the analysis of such fibrations, and we describe an…

We establish birational superrigidity for a large class of singular projective Fano hypersurfaces of index one. In the special case of isolated singularities, our result applies for instance to: (1) hypersurfaces with semi-homogeneous…

For a Zariski general (regular) hypersurface $V$ of degree $M$ in the $(M+1)$-dimensional projective space, where $M$ is at least 16, with at most quadratic singularities of rank at least 13, we give a complete description of the structures…

The elliptic curves on a surface of general type constitute an obstruction for the cotangent sheaf to be ample. In this paper, we give the classification of the configurations of the elliptic curves on the Fano surface of a smooth cubic…

In this paper we classify all configurations of singular fibers of elliptic fibrations on the double cover of P^2 ramified along six lines in general position.

We first classify the possible configurations of fibrations which are not semi-stable on extremal elliptic K3 surfaces. Then we give a complete list of extremal elliptic K3 surfaces whose singular fibers are all not of type $I_n$.

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 show that any quasismooth Fano threefold weighted complete intersections of type $(12, 14)$ in $\mathbb{P} (1, 2, 3, 4, 7, 11)$ is birationally solid.

We investigate fibrations by non-hyperelliptic curves of arithmetic genus three and geometric genus one in characteristic two. Assuming that there is only one moving singularity and that its image in the Frobenius pullback of the fibration…

We classify all pencils on a general weighted hypersurface in $\mathbb{P}(1,a_{1},a_{2},a_{3},a_{4})$ of degree $\sum_{i=1}^{4}a_{i}$ whose general members are surfaces of Kodaira dimension zero.

We survey some results on the nonrationality and birational rigidity of certain hypersurfaces of Fano type. The focus is on hypersurfaces of Fano index one, but hypersurfaces of higher index are also discussed.