Related papers: Notes on Fano varieties of complete intersections

We obtain criteria for detecting complete intersections in projective varieties. Motivated by a conjecture of Hartshorne concerning subvarieties of projective spaces, we investigate situations when two-codimensional smooth subvarieties of…

Tautological systems developed in [6],[7] are Picard-Fuchs type systems to study period integrals of complete intersections in Fano varieties. We generalize tautological systems to local complete intersections, which are zero loci of global…

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

We characterize building sets whose associated nonsingular projective toric varieties are Fano. Furthermore, we show that all such toric Fano varieties are obtained from smooth Fano polytopes associated to finite directed graphs.

We prove that a weak Fano manifold has unobstructed deformations. For a general variety, we investigate conditions under which a variety is necessarily obstructed.

This paper is a survey about cylinders in Fano varieties and related problems.

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.

The purpose of this note is to prove Grothendieck's standard conjectures for the Fano variety of lines on a smooth cubic hypersurface in projective space.

The map given by the anticanonical bundle of a Fano manifold is investigated with respect to a number of natural notions of higher order embeddings of projective manifolds. This is of importance in the understanding of higher order…

Let $Y$ be a smooth dimensionally transverse intersection of the Grassmannian $\hbox{Gr}(2,n)$ with 3 Pl\"ucker hyperplanes. We show that $Y$ admits a multiplicative Chow-K\"unneth decomposition, in the sense of Shen-Vial. As a consequence,…

We exhibit a large class of quiver moduli spaces which are Fano varieties, by studying line bundles on quiver moduli and their global sections in general, and work out several classes of examples, comprising moduli spaces of point…

Let $X$ be a Fano manifold which is the zero scheme of a general global section $s$ in an irreducible homogenous vector bundle over a Grassmannian. We prove that the restriction of the Pl\"ucker embedding embeds $X$ projectively normal, and…

This paper is to give some concrete examples of the general fibers of the evaluation map of some Kontsevich mapping spaces parametrize low degree rational curves on low degree complete intersection varieties. We prove these examples are…

We prove a characterization of Fano type varieties.

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…

Recently, the coupling of two different modes of a homogeneous plasmonic particle and their sharply varying spectra were elucidated as Fano resonances; an 'interference' of two spatially orthogonal modes driving each other. On the other…

We compute the quantum Euler class of Fano complete intersections X in a projective space. In particular, we prove a recent conjecture of A. Buch and R. Pandharipande. Finally we apply our result to obtain formulas for the virtual Tevelev…

In this paper, we obtain a complete classification of smooth toric Fano varieties equipped with extremal contractions which contract divisors to curves for any dimension. As an application, we obtain a complete classification of smooth…

We show that Fano lattice polygons define a class of balanced quivers with interesting properties. The combinatorics of these quivers is related to singularities of the underlying toric Fano surface. This allows us to show that every Fano…

We show that every reductive subgroup of the automorphism group of a quasi-smooth well formed weighted complete intersection is a restriction of a subgroup in the automorphism group in the ambient weighted projective space. Also, we provide…