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pro vyhledávání: '"Miró-Roig, Rosa M."'
The goal of this paper is to establish a new and efficient characterization of quasi-homogeneous isolated singularities of free curves and nearly free curves $C$ in $\mathbb{P}^2$. The criterion will be in terms of the first syzygy matrix associated
Externí odkaz:
http://arxiv.org/abs/2407.05819
Autor:
Mezzetti, Emilia, Miró-Roig, Rosa M.
In this paper, we determine the maximum $h_{max}$ and the minimum $h_{min}$ of the Hilbert vectors of Perazzo algebras $A_F$, where $F$ is a Perazzo polynomial of degree $d$ in $n+m+1$ variables. These algebras always fail the Strong Lefschetz Proper
Externí odkaz:
http://arxiv.org/abs/2405.14756
Autor:
Fantechi, Barbara, Miró-Roig, Rosa M.
Mukai proved that the moduli space of simple sheaves on a smooth projective K3 surface is symplectic, and in \cite{FM2} we gave two constructions allowing one to construct new locally closed Lagrangian/isotropic subspaces of the moduli from old ones.
Externí odkaz:
http://arxiv.org/abs/2403.00735
Autor:
Altafi, Nasrin, Di Gennaro, Roberta, Galetto, Federico, Grate, Sean, Miro-Roig, Rosa M., Nagel, Uwe, Seceleanu, Alexandra, Watanabe, Junzo
The connected sum construction, which takes as input Gorenstein rings and produces new Gorenstein rings, can be considered as an algebraic analogue for the topological construction having the same name. We determine the graded Betti numbers for conne
Externí odkaz:
http://arxiv.org/abs/2401.10492
Autor:
Kleppe, Jan O., Miró-Roig, Rosa M.
Let $\varphi: F\longrightarrow G$ be a graded morphism between free $R$-modules of rank $t$ and $t+c-1$, respectively, and let $I_j(\varphi)$ be the ideal generated by the $j \times j$ minors of a matrix representing $\varphi$. In this short note: (1
Externí odkaz:
http://arxiv.org/abs/2311.08008
The study of the Lefschetz properties of Artinian graded algebras was motivated by the hard Lefschetz theorem for a smooth complex projective variety, a breakthrough in algebraic topology and geometry. Over the last few years, this topic has attracte
Externí odkaz:
http://arxiv.org/abs/2311.03081
Autor:
Miró-Roig, Rosa M., Salat-Moltó, Martí
Let $(X,L)$ be a polarized smooth projective variety. For any basepoint-free linear system $\mathcal{L}_{V}$ with $V\subset H^{0}(X,\mathcal{O}_{X}(L))$ we consider the syzygy bundle $M_{V}$ as the kernel of the evaluation map $V\otimes \mathcal{O}_{
Externí odkaz:
http://arxiv.org/abs/2306.06713
Autor:
Fantechi, Barbara, Miró-Roig, Rosa M.
Let $X$ be a K3 surface and let $\text{Spl}(r;c_1,c_2)$ be the moduli space of simple sheaves on $X$ of fixed rank $r$ and Chern classes $c_1$ and $c_2$. Under suitable assumptions, to a pair $(F,W)$ (respectively, $(F,V)$) where $F\in \text{Spl}(r;c
Externí odkaz:
http://arxiv.org/abs/2306.05338
Autor:
Fantechi, Barbara, Miró-Roig, Rosa M.
Given a vector bundle $F$ on a variety $X$ and $W\subset H^0(F)$ such that the evaluation map $W\otimes \mathcal{O}_X\to F$ is surjective, its kernel $S_{F,W}$ is called generalized syzygy bundle. Under mild assumptions, we construct a moduli space $
Externí odkaz:
http://arxiv.org/abs/2306.04317
Autor:
Abdallah, Nancy, Altafi, Nasrin, De Poi, Pietro, Fiorindo, Luca, Iarrobino, Anthony, Marques, Pedro Macias, Mezzetti, Emilia, Miró-Roig, Rosa M., Nicklasson, Lisa
We study Hilbert functions, Lefschetz properties, and Jordan type of Artinian Gorenstein algebras associated to Perazzo hypersurfaces in projective space. The main focus lies on Perazzo threefolds, for which we prove that the Hilbert functions are al
Externí odkaz:
http://arxiv.org/abs/2303.16768