Related papers: Ueda theory for compact curves with nodes
We give sharp lower bounds for the postulation of the nodes of a general plane projection of a smooth connected curve C in P^r and we study the relationships with the geometry of the embedding. Strict connections with Castelnuovo's theory…
We study negative curves on surfaces obtained by blowing up special configurations of points in the complex projective palne. Our main results concern the following configurations: very general points on a cubic, 3-torsion points on an…
Let C be a 2-connected Gorenstein curve either reduced or contained in a smooth algebraic surface and let S be a subcanonical cluster (i.e. a 0-dim scheme such that the space H^0(C, I_S K_C) contains a generically invertible section). Under…
We construct examples of $C^\infty$ smooth submanifolds in ${\Bbb C}^n$ and ${\Bbb R}^n$ of codimension 2 and 1, which intersect every complex, respectively real, analytic curve in a discrete set. The examples are realized either as compact…
In this paper we compute the gonality and the dimension of the Brill-Noether loci $W^1_d(C)$ for curves in a non primitive linear system of a simple abelian surface, adapting vector bundles techniques \`a la Lazarsfeld originally introduced…
There are no known failures of Bounded Negativity in characteristic 0. In the light of recent work showing the Bounded Negativity Conjecture fails in positive characteristics for rational surfaces, we propose new characteristic free…
We study the family of irreducible curves with $\delta$ nodes belonging to a free linear system $|C|$ with smooth general member on a surface $S$ such that $|K_S|$ is ample. Under the assumption that $C$ is numerically equivalent to $pK_S$,…
We develop a new concept of non-positive curvature for metric spaces, based on intersection patterns of closed balls. In contrast to the synthetic approaches of Alexandrov and Buesemann, our concept also applies to metric spaces that might…
In this paper, we study the curve cone of an almost complex $4$-manifold which is tamed by a symplectic form. In particular, we prove the cone theorem as in Mori theory for all such manifolds using the Seiberg-Witten theory. For small…
We study curve singularities in a smooth surface relative to a smooth boundary curve. We consider the semiuniversal deformations and equisingular deformations of curves with a fixed local intersection number $w$ with the boundary, and prove…
Let $S$ be a complete flat surface, such as the Euclidean plane. We obtain direct characterizations of the connected components of the space of all curves on $S$ which start and end at given points in given directions, and whose curvatures…
These are lecture notes for a course to be held. They provide a full discussion of certain analytic aspects of the uniformisation theory of (singular) holomorphic foliations by curves on compact Kaehler manifolds, with emphasis on their…
We study the gonality and canonical model of a rational unicuspidal curve C. We are mainly interested in the case where C is non-Gorenstein. We classify such curves via different notions of gonality, and by its canonical model C', up to…
A first step towards a systematic theory of relative line bundles over SUSY-curves is presented. In this paper we deal with the case of relative line bundles over families of ordinary Riemann surfaces. Generalizations of the Gauss-Bonnet…
We obtain new examples and the complete list of the rational cuspidal plane curves $C$ with at least three cusps, one of which has multiplicity ${\rm deg}\,C - 2$. It occurs that these curves are projectively rigid. We also discuss the…
We study different notions of slope of a vector bundle over a smooth projective curve with respect to ampleness and affineness in order to apply this to tight closure problems. This method gives new degree estimates from above and from…
For a reductive group $G$, Harder-Narasimhan theory gives a structure theorem for principal $G$ bundles on a smooth projective curve $C$. A bundle is either semistable, or it admits a canonical parabolic reduction whose associated Levi…
We develop an intersection theory for a singular hemitian line bundle with positive curvature current on a smooth projective variety and irreducible curves on the variety. And we prove the existence of a natural rational fibration structure…
A quadric in $\R P^3$ cuts a curve of degree 6 on a cubic surface in $\R P^3$. The papers classifies the nonsingular curves cut in this way on non-singular cubic surfaces up to homeomorphism. Two issues new in the study related to the first…
A widely believed conjecture predicts that curves of bounded geometric genus lying on a variety of general type form a bounded family. One may even ask whether the canonical degree of a curve $C$ in a variety of general type is bounded from…