Related papers: Regularity of smooth curves in biprojective spaces

Let S=K[x_1,..., x_n], let A,B be finitely generated graded S-modules, and let m=(x_1,...,x_n). We give bounds for the Castelnuovo-Mumford regularity of the local cohomology of Tor_i(A,B) under the assumption that the Krull dimension of…

Throughout this paper we study the existence of irreducible curves C on smooth projective surfaces S with singular points of prescribed topological types S_1,...,S_r. There are necessary conditions for the existence of the type \sum_{i=1}^r…

We give a proof of the Gromov compactness theorem using the language of stable curves (i.e. cusp-curve of Gromov, or stable maps of Kontsevich and Manin) in general setting: An almost complex structure on a target manifold is only…

We prove that Allard's regularity theorem holds for rectifiable $n$-dimensional varifolds $V$ assuming a weaker condition on the first variation. This, in the special case when $V$ is a smooth manifold translates to the following: If…

Motivated by questions in interpolation theory and on linear systems of rational varieties, one is interested in upper bounds for the Castelnuovo-Mumford regularity of arbitrary subschemes of fat points. An optimal upper bound, named after…

We extend the results of Pareschi on the constancy of the gonality and Clifford index of smooth curves in a complete linear system on Del Pezzo surfaces of degrees $\geq 2$ to the case of Del Pezzo surfaces of degree 1, where we explicitly…

Let $(M,g)$ be a smooth connected Riemannian manifold. We show an improvement of flatness theorem for hypersurfaces of $M$ of bounded nonlocal mean curvature in the viscosity sense. It implies local $ C^{1,\alpha}$ regularity of these…

We prove optimal boundary $C^{1,\alpha}$ regularity for viscosity solutions of degenerate fully nonlinear uniformly elliptic equations with oblique boundary conditions and Hamiltonian terms of the form \[ \begin{cases} |Du|^{\gamma}F(D^2 u)…

In this article we study, given a pair of integers (d,g), the problem of existence of a smooth, irreducible, non-degenerate curve in the projective n-domensional space of degree d and genus g (the Halphen-Castelnuovo Problem). We define two…

We study the Betti numbers of binomial edge ideal associated to some classes of graphs with large Castelnuovo-Mumford regularity. As an application we give several lower bounds of the Castelnuovo-Mumford regularity of arbitrary graphs…

In this paper we prove that if $I(G)$ is a bipartite edge ideal with regularity three then for all $s\geq 2$ the regularity of $I(G)^s$ is exactly $2s+1$.

This note revisits stability conditions on the bounded derived categories of coherent sheaves on irreducible projective curves. In particular, all stability conditions on smooth curves are classified and a connected component of the…

Recently Bowden, Hensel and Webb defined the fine curve graph for surfaces, extending the notion of curve graphs for the study of homeomorphism or diffeomorphism groups of surfaces. Later Long, Margalit, Pham, Verberne and Yao proved that…

Connected bipartite graphs whose binomial edge ideals are Cohen--Macaulay have been classified by Bolognini et al. In this paper, we compute the depth, Castelnuovo--Mumford regularity, and dimension of the generalized binomial edge ideals…

Let $\mathcal C$ be a real plane algebraic curve defined by the resultant of two polynomials (resp. by the discriminant of a polynomial). Geometrically such a curve is the projection of the intersection of the surfaces $P(x,y,z)=Q(x,y,z)=0$…

The aim of this paper is to prove the existence of large complete subvarieties in moduli spaces of rank two stable sheaves with arbitrary $c_1$ and sufficiently large $c_2$ on algebraic surfaces. Then we study the restriction of these…

In this article, we obtain an upper bound for the Castelnuovo-Mumford regularity of powers of an ideal generated by a homogeneous quadratic sequence in a polynomial ring in terms of the regularity of its related ideals and degrees of its…

A good canonical projection of a surface $S$ of general type is a morphism to the 3-dimensional projective space P^3 given by 4 sections of the canonical line bundle. To such a projection one associates the direct image sheaf F of the…

We study the projective normality of a linearly normal special scroll R of degree d and speciality i over a smooth curve of genus g. If d>=4g-2i+1, we prove that the projective normality of the scroll is equivalent to the projective…

We study the Castelnuovo-Mumford regularity of the vanishing ideal over a bipartite graph endowed with a decomposition of its edge set. We prove that, under certain conditions, the regularity of the vanishing ideal over a bipartite graph…