Related papers: Fano threefolds in positive characteristic IV

We exhibit families of smooth projective threefolds with both stably rational and non stably rational fibers.

We prove the $W\mathcal{O}$-rationality of klt threefolds and the rational chain connectedness of klt Fano threefolds over a perfect field of characteristic $p>5$. As a consequence, any klt Fano threefold over a finite field has a rational…

We construct a family of Fano fourfolds with the derived category of coherent sheaves of a general Enriques surface as semiorthogonal component. This improves a result of Kuznetsov, lowering the Fano dimension of a general Enriques surface…

Given any field $k$ (not necessarily perfect), we study the smoothing of a semistable Fano variety over $k$. In characteristic 0, the reduced semistable Fano degenerate fibers of Mori fibrations are classified. In positive characteristic,…

We give an explicit construction of prime Fano threefolds of genus 12 with a $G_m$-action, describe their isomorphism classes and automorphism groups.

We prove that $\mathbb{Q}$-Fano threefolds of Fano index $\ge 8$ are rational.

We consider the structure of the derived categories of coherent sheaves on Fano threefolds with Picard number 1 and describe a strange relation between derived categories of different threefolds. In the Appendix we discuss how the ring of…

We study unirationality of actions of finite groups on Fano threefolds.

A classification theorem for 4-dimensional conformally flat QK3-manifolds is proved.

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

We observe a method for finding weak Landau-Ginzburg models for Fano varieties and find them for smooth Fano threefolds of genera 9, 10, and 12.

We classify some special classes of non-rational Fano threefolds with terminal singularities. In particular, all such hyperelliptic and trigonal varieties are found.

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 obtain upper bounds on the number of singular points of factorial terminal Fano threefolds.

We classify all possible automorphism groups of smooth cubic surfaces over an algebraically closed field of arbitrary characteristic. As an intermediate step we also classify automorphism groups of quartic del Pezzo surfaces. We show that…

Let $\mathcal{F}(n)$ be the set of smooth Fano $n$-polytopes up to unimocular equivalence. In this paper, we consider the F-equivalence or I-equivalence classes for $\mathcal{F}(n)$ and introduce F-isolated or I-isolated smooth Fano…

In this paper, we will show that the affine cones over any smooth Fano-Mukai fourfold of genus $7$ are flexible.

We study unirationality and rationality of Fano threefolds of degree 18 over nonclosed fields.

We prove that a general Fano hypersurface in a projective space over an algebraically closed field of arbitrary characteristic is separably rationally connected.