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pro vyhledávání: '"Ellia, Philippe"'
Autor:
Ellia, Philippe
Let C \in P2 be a reduced, singular curve of degree d and equation f = 0. Let \Sigma denote the jacobian subscheme of C. We have 0 -> E -> 3.O -> I_\Sigma(d-1) -> 0 (the surjection is given by the partials of f). We study the relationships between th
Externí odkaz:
http://arxiv.org/abs/1902.05472
Autor:
Ellia, Philippe
A closed subscheme of codimension two $T \subset P^2$ is a quasi complete intersection (q.c.i.) of type $(a,b,c)$ if there exists a surjective morphism $\mathcal{O} (-a) \oplus \mathcal{O} (-b) \oplus \mathcal{O} (-c) \to \mathcal{I} _T$. We give bou
Externí odkaz:
http://arxiv.org/abs/1901.00809
Autor:
Ellia, Philippe
We show that a normalized rank two vector bundle, E, on P2 splits if and only if h1(E(-1)) = 0. Using this fact we give another proof of a theorem of Chiantini and Valabrega. Finally we describe the normalized bundles with h1(E(-1)) <= 4.
Externí odkaz:
http://arxiv.org/abs/1901.00807
Autor:
Ballico, Edoardo, Ellia, Philippe
Fix positive integers d;m such that $(m^2+4m+6)/6 \leq d < (m^2+4m+6)/3$ (the so-called Range A for space curves). Let G(d;m) be the maximal genus of a smooth and connected curve, of degree d, $C \subset P^3$ such that $h^0(I_C(m-1)) = 0$. Here we pr
Externí odkaz:
http://arxiv.org/abs/1811.08807
We prove the following statement, which has been conjectured since 1985: There exists a constant $K$ such that for all natural numbers $d,g$ with $g\le Kd^{3/2}$ there exists an irreducible component of the Hilbert scheme of $\mathbb{P}^3$ whose gene
Externí odkaz:
http://arxiv.org/abs/1705.10113
Autor:
Ellia, Philippe, Menegatti, Paolo
Let A be a k-vector space of dimension a. A subvector space M of End(A) is said to be of rank r if every non-zero f in M has rank r. The problem considered in this paper is to determine l(r;a) the maximal dimension of a rank r subspace of End(A). Kno
Externí odkaz:
http://arxiv.org/abs/1508.00209
Autor:
Ellia, Philippe, Gruson, Laurent
We classify rank two vector bundles on P3 with Buchsbaum index equal to three and also give some results on the H1-module of "negative instanton"bundles.
Comment: Submitted to the proceedings of the Pau-Trieste conferences Vector bundles days
Comment: Submitted to the proceedings of the Pau-Trieste conferences Vector bundles days
Externí odkaz:
http://arxiv.org/abs/1503.02562
Autor:
Ellia, Philippe
A multiple (loc. Cohen Macaulay) structure, X, on a space curve C in P3 is said to be primitive if X is locally contained in a smooth surface. We give numerical conditions for C to be a "primitive" set theoretic complete intersection (i.e. to have a
Externí odkaz:
http://arxiv.org/abs/1409.3801
Autor:
Ellia, Philippe, Gruson, Laurent
Let E be a stable rank two normalized vector bundle on P3. If H is a general plane we show that h^0(E_H(1)) \leq 2+c_1. It follows that h^0(E(1)) \leq 2+c_1.
Comment: 5 pg
Comment: 5 pg
Externí odkaz:
http://arxiv.org/abs/1409.3789
Autor:
Ellia, Philippe, Menegatti, Paolo
We prove some results on the distance between two perfect numbers using Ramanujan-Nagell type equations.
Externí odkaz:
http://arxiv.org/abs/1406.2183