Zobrazeno 1 - 10
of 237
pro vyhledávání: '"Migliore, Juan"'
Autor:
Chiantini, Luca, Farnik, Łucja, Favacchio, Giuseppe, Harbourne, Brian, Migliore, Juan, Szemberg, Tomasz, Szpond, Justyna
In this note we introduce the notion of $(b,d)$-geprofi sets and study their basic properties. These are sets of $bd$ points in $\mathbb{P}^4$ whose projection from a general point to a hyperplane is a full intersection, i.e., the intersection of a c
Externí odkaz:
http://arxiv.org/abs/2407.01744
For artinian Gorenstein algebras in codimension four and higher, it is well known that the Weak Lefschetz Property (WLP) does not need to hold. For Gorenstein algebras in codimension three, it is still open whether all artinian Gorenstein algebras sa
Externí odkaz:
http://arxiv.org/abs/2406.17943
Autor:
Favacchio, Giuseppe, Migliore, Juan
Ideals $I\subseteq R=k[\mathbb P^n]$ generated by powers of linear forms arise, via Macaulay duality, from sets of fat points $X\subseteq \mathbb P^n$. Properties of $R/I$ are connected to the geometry of the corresponding fat points. When the linear
Externí odkaz:
http://arxiv.org/abs/2406.09571
Autor:
Chiantini, Luca, De Poi, Pietro, Farnik, Lucja, Favacchio, Giuseppe, Harbourne, Brian, Ilardi, Giovanna, Migliore, Juan, Szemberg, Tomasz, Szpond, Justyna
The purpose of this work is to pursue classification of geproci sets. Specifically we classify $[m,n]$-geproci sets which consist of $m=4$ points on each of $n$ skew lines, assuming the skew lines have two transversals in common. We show that in this
Externí odkaz:
http://arxiv.org/abs/2312.04644
Autor:
Migliore, Juan, Nagel, Uwe
Freeness is an important property of a hypersurface arrangement, although its presence is not well understood. A hypersurface arrangement in $\PP^n$ is free if $S/J$ is Cohen-Macaulay (CM), where $S = K[x_0,\ldots,x_n]$ and $J$ is the Jacobian ideal.
Externí odkaz:
http://arxiv.org/abs/2312.01192
Autor:
Chiantini, Luca, Farnik, Łucja, Favacchio, Giuseppe, Harbourne, Brian, Migliore, Juan, Szemberg, Tomasz, Szpond, Justyna
Geproci sets of points in $\mathbb P^3$ are sets whose general projections to $\mathbb P^2$ are complete intersections. The first nontrivial geproci sets came from representation theory, as projectivizations of the root systems $D_4$ and $F_4$. In mo
Externí odkaz:
http://arxiv.org/abs/2308.00761
Autor:
Chiantini, Luca, Farnik, Lucja, Favacchio, Giuseppe, Harbourne, Brian, Migliore, Juan, Szemberg, Tomasz, Szpond, Justyna
In this short note we develop new methods toward the ultimate goal of classifying geproci sets in $\mathbb P^3$. We apply these methods to show that among sets of $16$ points distributed evenly on $4$ skew lines, up to projective equivalence there ar
Externí odkaz:
http://arxiv.org/abs/2303.16263
The notion of an unexpected curve in the plane was introduced in 2018, and was quickly generalized in several directions in a flurry of mathematical activity by many authors. In this expository paper we first describe some of the main results on unex
Externí odkaz:
http://arxiv.org/abs/2303.13317
We consider the conjecture that all artinian height 4 complete intersections of forms of the same degree $d$ have the Weak Lefschetz Property (WLP). We translate this problem to one of studying the general hyperplane section of a certain smooth curve
Externí odkaz:
http://arxiv.org/abs/2212.09890
Autor:
Chiantini, Luca, Farnik, Łucja, Favacchio, Giuseppe, Harbourne, Brian, Migliore, Juan, Szemberg, Tomasz, Szpond, Justyna
We call a set of points $Z\subset{\mathbb P}^{3}_{\mathbb C}$ an $(a,b)$-geproci set (for GEneral PROjection is a Complete Intersection) if its projection from a general point $P$ to a plane is a complete intersection of curves of degrees $a$ and $b$
Externí odkaz:
http://arxiv.org/abs/2209.04820