We use orbifold structures to deduce degeneracy statements for holomorphic maps into logarithmic surfaces. We improve former results in the smooth case and generalize them to singular pairs. In particular, we give applications on nodal surfaces and complements of singular plane curves.
We prove that the bounded derived category of the surface constructed by Barlow admits a length 11 exceptional sequence consisting of (explicit) line bundles. Moreover, we show that in a small neighbourhood of in the moduli space of determinantal Barlow surfaces, the generic surface has a semiorthogonal decomposition of its derived category into a length 11 exceptional sequence of line bundles and a category with trivial Grothendieck group and Hochschild homology, called a phantom category....
First we find effective bounds for the number of dominant rational maps between two fixed smooth projective varieties with ample canonical bundles. The bounds are of the type , where , is the canonical bundle of and are some constants, depending only on .Then we show that for any variety there exist numbers and with the following properties:For any threefold of general type the number of dominant rational maps is bounded above by .The number of threefolds , modulo birational...
In questo lavoro si generalizzano alcuni risultati di [3] riguardanti la proprietà di alcune curve nodali, su superficie non-singolari in , di essere «geometricamente linearmente normali» (concetto che estende la ben nota proprietà di essere linearmente normale). Precisamente, per una data curva , irriducibile e dotata di soli punti nodali come uniche singolarità, che giace su una superfice proiettiva, non-singolare e linearmente normale, si determina un limite superiore «sharp» sul numero dei...
In 1981 J. Noguchi proved that in a logarithmic algebraic manifold, having logarithmic irregularity strictly bigger than its dimension, any entire curve is algebraically degenerate.In the present paper we are interested in the case of manifolds having logarithmic irregularity equal to its dimension. We restrict our attention to Brody curves, for which we resolve the problem completely in dimension 2: in a logarithmic surface with logarithmic irregularity and logarithmic Kodaira dimension , any...
We give explicit constructions of all the numerical Campedelli surfaces, i.e. the minimal surfaces of general type with and , whose fundamental group has order 9. There are three families, one with and two with . We also determine the base locus of the bicanonical system of these surfaces. It turns out that for the surfaces with and for one of the families of surfaces with the base locus consists of two points. To our knowlegde, these are the only known examples of surfaces of general...