Related papers: Severi type inequalities for irregular surfaces wi…

The present work deals with the canonical map of smooth, compact complex surfaces of general type in a polarization of type $(1,2,2)$ on an abelian threefold. A natural and classical question is whether the canonical system of such surfaces…

For a line bundle L on a smooth surface S, it is now known that the degree of the Severi variety of cogenus-d curves is given by a universal polynomial in the Chern classes of L and S if L is d-very ample. For S rational, we relax the…

Let V be a smooth quasi-projective complex surface such that the three first logarithmic plurigenera are equal to 1 and the logarithmic irregularity is equal to 2. We prove that the quasi-Albanese morphism of V is birational and there…

We give a new construction of the irregular, generalized Lagrangian, surfaces of general type with p_g=5, \chi=2, K^2=8, recently discovered by Chad Schoen. Our approach proves that, if S is a general Schoen surface, its canonical map is a…

This paper is devoted to the classification of irregular surfaces of general type with $p_g=q=2$ and non birational bicanonical map. The main result is that, if $S$ is such a surface and if $S$ is minimal with no pencil of curves of genus…

Given a minimal surface equipped with a generically finite map to an Abelian variety, we give an optimal bound on the canonical degree of a rational or an elliptic curve. As a corollary, we obtain the finiteness of rational and elliptic…

Minimal irregular surfaces of general type satisfy K^2\geq 2p_g. In this paper we classify those surfaces for which the equality K^2=2p_g holds.

Let X be a complex projective n-dimensional manifold of general type, whose canonical system is composite with a pencil. If the Albanese map is generically finite, but not surjective, or if the irregularity is strictly larger than n and the…

Let $S$ be a minimal irregular surface of general type, whose Albanese map induces a hyperelliptic fibration $f:\,S \to B$ of genus $g$.We prove a quadratic upper bound on the genus $g$, i.e., $g\leq h\big(\chi(\mathcal{O}_S)\big)$, where…

We construct a connected, irreducible component of the moduli space of minimal surfaces of general type with $p_g=q=2$ and $K^2=5$, which contains both examples given by Chen-Hacon and the first author. This component is generically smooth…

Self-rational maps of generic algebraic K3 surfaces are conjectured to be trivial. We relate this conjecture to a conjecture concerning the irreducibility of the universal Severi varieties parametrizing nodal curves of given genus and…

We study and obtain Slope inequalities for fibred irregular varieties of non-maximal Albanese dimension. We give a comparison theorem between Clifford-Severi and Slope inequalities for this type of fibrations. We also obtain a set of Slope…

In this note, we construct two minimal surfaces of general type with geometric genus p_g= 3, irregularity q = 0, self-intersection of the canonical divisor K^22 =20,24 such that their canonical map is of degree 20. In one of these surfaces,…

In this paper, we classify the minimal surfaces of general type with $\chi=5$, $K^{2}=9$ whose canonical map is composed with an involution. We obtain 6 families, whose dimensions in the moduli space are 28, 27, 33, 32, 31 and 32…

We prove effective upper bounds on the global sections of nef line bundles of small generic degree over a fibered surface over a field of any characteristic. It can be viewed as a relative version of the classical Noether inequality for…

For a linear system $|C|$ on a smooth projective surface $S$, whose general element is a smooth, irreducible curve, the Severi variety $V_{|C|, \delta}$ is the locally closed subscheme of $|C|$ which parametrizes irreducible curves with…

We use the Borisov-Keum equations of a fake projective plane and the Borisov-Yeung equations of the Cartwright-Steger surface to show the existence of a regular surface with canonical map of degree 36 and of an irregular surface with…

We construct a new family of minimal surfaces of general type with $p_g=q=2$ and $K^2=6$, whose Albanese map is a quadruple cover of an abelian surface with polarization of type $(1,3)$. We also show that this family provides an irreducible…

In this note, we make a step towards the classification of toric surfaces admitting reducible Severi varieties. We generalize the results of [Lan19, Tyo13, Tyo14], and provide two families of toric surfaces admitting reducible Severi…

Let $X$ be a smooth complex projective variety such that the Albanese map of $X$ is generically finite onto its image. Here we study the so-called eventual $m$-paracanonical map of $X$ (when $m=1$ we also assume $\chi(K_X)>0$). We show that…