Zobrazeno 1 - 10
of 240
pro vyhledávání: '"Conca, Aldo"'
We consider ideals in a polynomial ring generated by collections of power sum polynomials, and obtain conditions under which these define complete intersection rings, normal domains, and unique factorization domains. We also settle a key case of a co
Externí odkaz:
http://arxiv.org/abs/2409.18906
For $K$ an infinite field of characteristic other than two, consider the action of the special orthogonal group $\operatorname{SO}_t(K)$ on a polynomial ring via copies of the regular representation. When $K$ has characteristic zero, Boutot's theorem
Externí odkaz:
http://arxiv.org/abs/2406.14439
Autor:
Conca, Aldo
In 1965 Buchberger defined Gr\"obner bases and an algorithm to compute them. Despite a slow start, already in the eighties Gr\"obner bases had become the main device for symbolic computations involving polynomials as well as a theoretical tool for th
Externí odkaz:
http://arxiv.org/abs/2403.07098
Autor:
Conca, Aldo, Tsakiris, Manolis C.
Let $X$ be the union of $n$ generic linear subspaces of codimension $>1$ in $\mathbb{P}^d$. Improving an earlier bound due to Derksen and Sidman, we prove that the Castelnuovo-Mumford regularity of $X$ satisfies $ \operatorname{reg}(X) \le n - [n / (
Externí odkaz:
http://arxiv.org/abs/2402.02305
Autor:
Conca, Aldo
Let $R$ be a finitely generated $\mathbb N$-graded algebra domain over a Noetherian ring and let $I$ be a homogeneous ideal of $R$. Given $P\in Ass(R/I)$ one defines the $v$-invariant $v_P(I)$ of $I$ at $P$ as the least $c\in \mathbb N$ such that $P=
Externí odkaz:
http://arxiv.org/abs/2401.00022
A Taylor variety consists of all fixed order Taylor polynomials of rational functions, where the number of variables and degrees of numerators and denominators are fixed. In one variable, Taylor varieties are given by rank constraints on Hankel matri
Externí odkaz:
http://arxiv.org/abs/2304.00712
Autor:
Bruns, Winfried, Conca, Aldo
The maximal minors of a matrix of indeterminates are a universal Gr\"obner basis by a theorem of Bernstein, Sturmfels and Zelevinsky. On the other hand it is known that they are not always a universal Sagbi basis. By an experimental approach we discu
Externí odkaz:
http://arxiv.org/abs/2302.14345
We study several properties of multihomogeneous prime ideals. We show that the multigraded generic initial ideal of a prime has very special properties, for instance, its radical is Cohen-Macaulay. We develop a comprehensive study of multidegrees in
Externí odkaz:
http://arxiv.org/abs/2208.07238
Can one tell if an ideal is radical just by looking at the degrees of the generators? In general, this is hopeless. However, there are special collections of degrees in multigraded polynomial rings, with the property that any multigraded ideal genera
Externí odkaz:
http://arxiv.org/abs/2203.08732
Autor:
Cioffi, Francesca, Conca, Aldo
We prove a doubly exponential bound for the Castelnuovo-Mumford regularity of prime ideals defining varieties with polynomial parametrisation.
Comment: To appear in Annali della Scuola Normale Superiore di Pisa, Classe di Scienze
Comment: To appear in Annali della Scuola Normale Superiore di Pisa, Classe di Scienze
Externí odkaz:
http://arxiv.org/abs/2202.07696