Related papers: Non-degenerate curves with maximal Hartshorne-Rao …

By means of an {\it ad hoc} modification of the so-called ``Castelnuovo-Harris analysis" we derive an upper bound for the genus of integral curves on the three dimensional nonsingular quadric which lie on an integral surface of degree $2k$,…

For a finitely generated graded module $M$ over a positively-graded commutative Noetherian ring $R$, the second author established in 1999 some restrictions, which can be formulated in terms of the Castelnuovo regularity of $M$ or the…

Let $R$ be a Noetherian ring, $I$ an ideal of $R$ and $M$ an $R$-module with $\operatorname{cd}(I,M)=c$. In this article, we first show that there exists a descending chain of ideals $I=I_c\supsetneq I_{c-1}\supsetneq \cdots \supsetneq I_0$…

Let X be a smooth irreducible complex projective curve of genus g > 1. In this paper, we give necessary and sufficient conditions for an unstable bundle of HN-lenght 2 to have a particular algebra of endomorphisms. Then, fixing the…

The present work is concerned with characterizing some algebraic invariants of edge ideals of hypergraphs. To this aim, firstly, we introduce some kinds of combinatorial invariants similar to matching numbers for hypergraphs. Then we…

Let $M$ be the moduli space of rank $2$ stable bundles with fixed determinant of degree $1$ on a smooth projective curve $C$ of genus $g\ge 2$. When $C$ is generic, we show that any elliptic curve on $M$ has degree (respect to…

We show that mapping class groups associated to all types of real algebraic curves are virtual duality groups. We also deduce some results about the orbifold homotopy groups of the moduli spaces of real algebraic curves. We achieve these…

We show that the moduli space of degree $e$ maps from smooth genus $g \ge 1$ curves to an arbitrary low degree smooth hypersurface is singular when $e$ is large compared to $g$. We also give a lower bound for the dimension of the singular…

We classify invariant curves for birational surface maps that are expanding on cohomology. When the expansion is exponential, the arithmetic genus of an invariant curve is at most one. This implies severe constraints on both the type and…

We prove that the moduli spaces of rational curves of degree at most $3$ in linear sections of the Grassmannian $Gr(2,5)$ are all rational varieties. We also study their compactifications and birational geometry.

We investigate the geometry of the graphs of nonseparating curves for surfaces of finite positive genus with potentially infinitely many punctures. This graph has infinite diameter and is known to be Gromov hyperbolic by work of the author.…

We study a space of genus $g$ stable, $n$-marked tropical curves with total edge length $1$. Its rational homology is identified both with top-weight cohomology of the complex moduli space $M_{g,n}$ and with the homology of a marked version…

We construct a degeneration of the moduli space of Hitchin pairs on smooth projective curves when the curve degenerates to an irreducible curve with a single node. The degeneration constructed here is analogous to the models constructed by…

In this paper, we study combinatorial properties of stable curves. To the dual graph of any nodal curve, it is naturally associated a group, which is the group of components of the N\'eron model of the generalized Jacobian of the curve. We…

This note is about invariants of moduli spaces of curves. It includes their intersection theory and cohomology. Our main focus in on the distinguished piece containing the so called tautological classes. These are the most natural classes…

In this note, we establish the following Second Main Theorem type estimate for every entire non-algebraically degenerate holomorphic curve $f\colon\mathbb{C}\rightarrow\mathbb{P}^n(\mathbb{C})$, in present of a {\sl generic} hypersuface…

In this paper we prove the following generalization of a result of Hartshorne: Let $(S,\n)$ be a regular local ring of dimension $4$. Assume that $x,y,u,v$ is a regular system of parameters for $S$ and $a:=xu+yv$. Then for each finitely…

We make explicit computations in the formal symplectic geometry of Kontsevich and determine the Euler characteristics of the three cases, namely commutative, Lie and associative ones, up to certain weights.From these, we obtain some…

The goal of this paper is to explicitly detect all the arithmetic genera of arithmetically Cohen-Macaulay projective curves with a given degree $d$. It is well-known that the arithmetic genus $g$ of a curve $C$ can be easily deduced from…

We present algorithms for parametrizing by radicals an irreducible curve, not necessarily plane, when the genus is less o equal to 4 and they are defined over an algebraically closed field of characteristic zero. In addition, we also…