Related papers: Gorenstein Fano threefolds with base points in the…
In this paper, we study the explicit geography problem of irregular Gorenstein minimal 3-folds of general type. We generalize the classical Noether-Castelnuovo inequalities for irregular surfaces to irregular 3-folds according to the…
We study a useful numerical invariant of normal surface singularities, introduced recently by T. Kawachi. Using this invariant, we give a quick proof of the (well-known) fact that all log-canonical surface singularities are either elliptic…
A canonical system of basic invariants is a system of invariants satisfying a set of differential equations. The properties of a canonical system are related to the mean value property for polytopes. In this article, we naturally identify…
In this paper we propose an approach to investigate the canonical rings of surfaces of general type whose canonical system has isolated base points and yields a birational map onto its image. We apply then the method in the concrete case of…
We rework the Mori-Mukai classification of Fano 3-folds, by describing each of the 105 families via biregular models as zero loci of general global sections of homogeneous vector bundles over products of Grassmannians.
We study the anti-canonical ring of a projective variety and we characterise varieties of log Fano type depending on the singularities of these models.
We construct well-formed and quasismooth terminal Fano 4-folds of index 1 in low codimension containing at worst isolated orbifold points. We provide a certain classification of these varieties where their images under the anitcanonical…
In continuation of our paper in Math. Ann. 333 we classify smooth complex projective threefolds X with -K_X big and nef but not ample and Picard number 2, whose anticanonical map is small. We assume also that the Mori contraction of X and…
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…
A Fano-Enriques threefold is a three-dimensional non-Gorenstein Fano variety of index 1 with at most canonical singularities. We study the birational geometry of Fano-Enriques threefolds with terminal cyclic quotient singularities. We…
This article constructs a smooth weak Fano threefold of Picard number two with small anti-canonical morphism that arises as a blowup of a smooth curve of genus 5 and degree 8 in $\mathbb{P}^3$. While the existence of this weak Fano was…
Using a construction due to C. Casagrande and further developed by the author, we prove that the Picard number of a non-smooth Fano 3-fold with isolated factorial canonical singularities, is at most 6.
This paper studies the birational geometry of terminal Gorenstein Fano 3-folds. If Y is not Q-factorial, in most cases, it is possible to describe explicitly the divisor class group Cl Y by running a Minimal Model Program (MMP) on X, a…
We give a complete classification of smooth, complex projective Fano 4-folds of Picard number 3 having a prime divisor of Picard number 1. They form 28 distinct families, and we compute the main numerical invariants, study the base locus of…
We construct examples of threefolds with terminal singularities (resp. surfaces with canonical singularities) which are special in the sense of Campana, have a potentially dense set of integral points, admit a dense entire curve, have…
Let X be a compact K\"ahler manifold such that the anticanonical bundle $-K_X$ is nef. A classical conjecture claims that the Albanese map is submersive. We prove this conjecture if the general fibre is a weak Fano manifold. If X is…
We characterise smooth curves in P^3 whose blow-up produces a threefold with anticanonical divisor big and nef. These are curves C of degree d and genus g lying on a smooth quartic, such that (i) $4d-30 \le g\le 14$ or $(g,d) = (19,12)$,…
T.Kishimoto raised the problem to classify all compactifications of contractible affine 3-folds into smooth Fano 3-folds with second Betti number two and classified such compactifications whose log canonical divisors are not nef. In this…
In this paper, we show that Fujita's basepoint-freeness conjecture for projective quasi-log canonical singularities holds true in dimension three. Immediately, we prove Fujita-type basepoint-freeness for projective semi-log canonical…
For a terminal weak $\mathbb{Q}$-Fano $3$-fold $X$, we show that the $m$-th anti-canonical map defined by $|-mK_X|$ is birational for all $m\geq59$.