相关论文: Postulation of lines in P3 revisited

The Hartshorne--Hirschowitz theorem says that a generic union of lines in $\mathbb{P}^n$, $(n\geq 3)$, has good postulation. The proof of Hartshorne and Hirschowitz in the initial case $\mathbb{P}^3$ is difficult and so long, which is…

A well-known theorem by Hartshorne--Hirschowitz (\cite{HH}) states that a generic union $\mathbb{X}\subset \PP^n$, $n\geq 3$, of lines has good postulation with respect to the linear system $|\OO_{\PP^n}(d)|$. So a question that arises…

In this note we show that the union of $r$ general lines and one fat line in ${\mathbb P}^3$ imposes independent conditions on forms of sufficiently high degree $d$, where the bound on $d$ is independent of the number of lines. This extends…

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…

Robin Hartshorne and Alexander Hirschowitz proved that a generic collection of lines on $\mathbb P^n$, $n \geq 3$, has bipolynomial Hilbert Function. We extended this result to a specialization of the collection of generic lines, by…

We study the postulation of 0-dimensional schemes given by unions of 2-superfat points in general position in the plane, i.e., the union of local schemes defined by the intersection of two distinct double lines. We prove that such schemes…

In this paper we address the postulation problem of zero-dimensional schemes on a surface of length at most 4. We prove some general results and then we focus on the case of P2, P1xP1 and Hirzebruch surfarces. In particular, we prove that…

Projective spaces for finite-dimensional vector spaces over general fields are considered. The geometry of these spaces and the theory of line bundles over these spaces is presented. Particularly, the space of global regular sections of…

We describe the dimensions of Hochschild (co)homology groups of weighted projective curves over complex numbers. Surprisingly, all but one of those numbers depend only on the genus of the underlying non-weighted curve and the number of…

The main goal of this note is to begin a systematic study on conic-line arrangements in the complex projective plane. We show a de Bruijn-Erd\H{o}s-type inequality and Hirzebruch-type inequality for a certain class of conic-line…

We study the postulation of a general union $X\subset \mathbb {P}^3$ of one m-point $mP$ and $t$ disjoint lines. We prove that it has the expected Hilbert function, proving a conjecture by E. Carlini, M. V. Catalisano and A. V. Geramita.

We present a proof of the Harbourne-Hirschowitz conjecture for linear systems with base points of multiplicity seven or less. This proof uses a well-known degeneration of the projective plane, as well as a combinatorial technique that…

In this paper we prove the equivalence of two conjectures on linear systems through fat points on a generic K3 surface. The first conjecture is exactly as Segre conjecture on the projective plane. Whereas the second characterizes such…

Using the Klein correspondence, regular parallelisms of PG(3,R) have been described by Betten and Riesinger in terms of a dual object, called a hyperflock determining (hfd) line set. In the special case where this set has a span of…

The correspondence between 2-parameter families of oriented lines in ${\Bbb{R}}^3$ and surfaces in $T{\Bbb{P}}^1$ is studied, and the geometric properties of the lines are related to the complex geometry of the surface. Congruences…

We study the postulation of a general union Y of double, triple, quartuple and quintuple points of P^3. In characteristic 0, we prove that Y has good postulation in degree $d\ge 11$. The proof is based on the combination of the Horace…

We offer an axiomatic presentation of three-dimensional projective space that adopts the line as its fundamental element and renders automatic the principle of duality.

We endow the set of complements of a fixed subspace of a projective space with the structure of an affine space, and show that certain lines of such an affine space are affine reguli or cones over affine reguli. Moreover, we apply our…

We prove well-posedness in $L^2$-based Sobolev spaces $H^s$ at high regularity for a class of nonlinear higher-order dispersive equations generalizing the KdV hierarchy both on the line and on the torus.

This paper is devoted to the well-posedness of the inhomogeneous nonlinear wave equations. By combining Strichartz estimates with the contraction mapping principle, we establish local and global well-posedness in the function spaces…