Related papers: Cylinders in Fano varieties

This paper is devoted to a discussion of specific properties of invariants in the theory of forms.

We classify three-dimensional Fano varieties with canonical Gorenstein singularities of degree bigger than 64.

We classify Q-Fano threefolds of Fano index > 2 and big degree.

We construct several new families of Fano varieties of K3 type. We give a geometrical explanation of the K3 structure and we link some of them to projective families of irreducible holomorphic symplectic manifolds.

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…

We prove that the Satake-Baily-Borel compactification of certain Shimura varieties are Fano varieties, Calabi-Yau varieties or have ample canonical divisors with mild singularities. We also prove some variants statements, give applications…

We study the Picard variety of the Fano surface of nodal and mildly cuspidal cubic threefolds in arbitrary characteristic by relating divisors on the Fano surface to divisors on the symmetric product of a curve of genus 4.

We investigate Gorenstein toric Fano varieties by combinatorial methods using the notion of a reflexive polytope which appeared in connection to mirror symmetry. The paper contains generalisations of tools and previously known results for…

The goal of this paper is to explore the genus and degree of the Fano scheme of linear subspaces on a complete intersection in a complex projective space. Firstly, suppose that the expected dimension of the Fano scheme is one, we prove a…

In this paper, we will continue the investigation of Waring's problem, and give further improvements.

We exhibit full exceptional collections of vector bundles on any smooth, Fano arithmetic toric variety whose split fan is centrally symmetric.

This is an overview article on finite type invariants, written for the Encyclopedia of Mathematical Physics

We construct examples of Fano manifolds, which are defined over a field of positive characteristic, but not over $\com$.

We investigate the relationship between the Fano type property on fibers over a Zariski dense subset and the global Fano type property. We establish the invariance of N\'eron-Severi spaces, nef cones, effective cones, movable cones, and…

In this paper we classify n-dimensional Fano manifolds with index >=n-2 and positive second Chern character.

Conjecturally, Fano varieties of K3 type admit a multiplicative Chow-K\"unneth decomposition, in the sense of Shen-Vial. We prove this for many of the families of Fano varieties of K3 type constructed by Fatighenti-Mongardi. This has…

We give the first examples of flat fiber type contractions of Fano manifolds onto varieties that are not weak Fano, and we prove that these morphisms are Fano conic bundles. We also review some known results about the interaction between…

We determine the stability/instability of the tangent bundles of the Fano varieties in a certain class of two orbit varieties, which are classified by Pasquier in 2009. As a consequence, we show that some of these varieties admit unstable…

We survey what is known about Fano threefold weighted complete intersections from the point of view of birational rigidity.

This survey article is an accompaniment to the 2025 Summer Research Institute in Algebraic Geometry Bootcamp on K-stability and K-moduli. It is aimed at graduate students and intended to provide the necessary background to begin research on…