Related papers: Unbounded negativity on rational surfaces in posit…

In this paper, we prove the following "Weak Bounded Negativity Conjecture", which says that given a complex smooth projective surface $X$, for any reduced curve $C$ in $X$ and integer $g$, assume that the geometric genus of each component…

We give a theorem on the effective non-vanishing problem for algebraic surfaces in positive characteristic. For the Kawamata-Viehweg vanishing, the logarithmic Kollar vanishing and the logarithmic semipositivity, we give their…

We address the problem of bounding from below the self-intersection of integral curves on the projective plane blown-up at general points. In particular, by applying classical deformation theory we obtain the expected bound in the case of…

Let X be the blow-up of the projective plane in a finite set of very general points. We deduce from the work of Uehara that X has only standard autoequivalences, no nontrivial Fourier-Mukai partners, and admits no spherical objects. If X is…

Let $(X,D)$ be a pair where $X$ is a projective variety. We study in detail how the behavior of rational curves on $X$ as well as the positivity of $-(K_X+D)$ and $D$ influence the behavior of rational curves on $D$. In particular we give…

We show the existence of a rational surface automorphism of positive entropy with a given number of Siegel disks. Moreover, among automorphisms obtained from quadratic birational maps on the projective plane fixing irreducible cubic curves,…

In characteristic $p>0$ and for $q$ a power of $p$, we compute the number of nonplanar rational curves of arbitrary degrees on a smooth Hermitian surface of degree $q+1$ under the assumption that the curves have a parametrization given by…

A determination of the fixed components, base points and irregularity is made for arbitrary numerically effective divisors on any smooth projective rational surface having an effective anticanonical divisor. All of the results are proven…

We study the bounded negativity conjecture for non-quaternionic Hilbert modular surfaces and give an explicit bound for the special case of Hirzebruch-Zagier curves on Hilbert modular surfaces.

We show that Serre's Intersection Multiplicity Conjecture holds for a formal power series ring A over a complete, two-dimensional regular local ring R. From this, we deduce the corresponding result for the local rings of any scheme X which…

In this paper we give a necessary combinatorial condition for a negative--definite plumbing tree to be suitable for rational blow--down, or to be the graph of a complex surface singularity which admits a rational homology disk smoothing.…

We show that if a compact complex surface admits a locally conformally flat metric, then it cannot contain a smooth rational curve of odd self-intersection. In particular, the surface has to be minimal. Then we give a list of possibilities…

We construct a smooth and projective surface over an arbitrary number field that is a counterexample to the Hasse principle but has the infinite etale Brauer-Manin set. We also construct a surface with a unique rational point and the…

In this paper, we examine Green and Lazarsfeld's Np property for rational surfaces obtained by blowing up the projective plane P^2 at a subscheme of fat points Z. We show that these surfaces, embedded into projective spaces by linear system…

We study polarized cylinders in certain rational surfaces arising from blow-ups of weighted projective planes. In particular, we consider the surfaces obtained by blowing up $m+4$ points in general position on the weighted projective plane…

We begin by formally defining n-Tango curves and n-Raynaud surfaces. Our investigation then focuses on the pathological behaviors exhibited by n-Raynaud surfaces. As a direct corollary of this analysis, we present a concise disproof of…

We prove that there is a projective K3 surface admitting a (fixed point) free automorphism of positive entropy and that no smooth compact K\"ahler surface other than projective K3 surfaces and their blow up admits such an automorphism.

We study the rationality of some geometrically rational three-dimensional conic and quadric surface bundles, defined over the reals and more general real closed fields, for which the real locus is connected and the intermediate Jacobian…

In this note we exhibit the so-called Harbourne constants which capture and measure the Bounded Negativity on various birational models of an algebraic surface. We show an estimation for Harbourne constants for conic configurations on the…

We effectively bound T-singularities on non-rational projective surfaces with an arbitrary amount of T-singularities and ample canonical class. This fully generalizes the previous work for the case of one singularity, and illustrates the…