The Minimal Free Resolution of Fat Almost Complete Intersections in ℙ1 × ℙ1

2017 ◽  
Vol 69 (6) ◽  
pp. 1274-1291 ◽  
Author(s):  
Giuseppe Favacchio ◽  
Elena Guardo
Keyword(s):  
Complete Intersection ◽  
Free Resolution ◽  
Complete Intersections ◽  
Minimal Free Resolution ◽  
Symbolic Powers ◽  
Research Theme ◽  
Homogeneous Set ◽  
Triple Points ◽  
Set Of Points ◽  
A Current

AbstractA current research theme is to compare symbolic powers of an ideal I with the regular powers of I. In this paper, we focus on the case where I = IX is an ideal deûning an almost complete intersection (ACI) set of points X in ℙ1 × ℙ1. In particular, we describe a minimal free bigraded resolution of a non-arithmetically Cohen-Macaulay (also non-homogeneous) set 𝒵 of fat points whose support is an ACI, generalizing an earlier result of Cooper et al. for homogeneous sets of triple points. We call 𝒵 a fat ACI.We also show that its symbolic and ordinary powers are equal, i.e, .

Branched Coverings and Minimal Free Resolution for Infinite-Dimensional Complex Spaces

2003 ◽  
Vol 10 (1) ◽  
pp. 37-43
Author(s):  
E. Ballico
Keyword(s):  
Projective Space ◽  
Projective Spaces ◽  
Free Resolution ◽  
Complete Intersections ◽  
Vanishing Theorem ◽  
Sheaf Cohomology ◽  
Minimal Free Resolution ◽  
Branched Coverings ◽  
Infinite Dimensional ◽  
Complex Spaces

Abstract We consider the vanishing problem for higher cohomology groups on certain infinite-dimensional complex spaces: good branched coverings of suitable projective spaces and subvarieties with a finite free resolution in a projective space P(V ) (e.g. complete intersections or cones over finitedimensional projective spaces). In the former case we obtain the vanishing result for H 1. In the latter case the corresponding results are only conditional for sheaf cohomology because we do not have the corresponding vanishing theorem for P(V ).

scholarly journals Free resolutions of Dynkin format and the licci property of grade $3$ perfect ideals

2019 ◽  
Vol 125 (2) ◽  
pp. 163-178
Author(s):  
Lars Winther Christensen ◽  
Oana Veliche ◽  
Jerzy Weyman
Keyword(s):  
Recent Work ◽  
Local Ring ◽  
Complete Intersection ◽  
Dynkin Diagram ◽  
Free Resolution ◽  
Free Resolutions ◽  
Regular Local Ring ◽  
Minimal Free Resolution ◽  
Grade 3

Recent work on generic free resolutions of length $3$ attaches to every resolution a graph and suggests that resolutions whose associated graph is a Dynkin diagram are distinguished. We conjecture that in a regular local ring, every grade $3$ perfect ideal whose minimal free resolution is distinguished in this way is in the linkage class of a complete intersection.

On the configurations of codimension two linear subspaces of ℙN with the Waldschmidt constant less than 2

2020 ◽  
pp. 2150178
Author(s):  
Hassan Haghighi ◽  
Mohammad Mosakhani
Keyword(s):  
Hilbert Function ◽  
Free Resolution ◽  
Minimal Free Resolution ◽  
Codimension Two ◽  
Symbolic Powers ◽  
Point Configurations ◽  
Higher Dimensional ◽  
Algebraic Invariants ◽  
Waldschmidt Constants ◽  
Waldschmidt Constant

The purpose of this note is to generalize a result of [M. Dumnicki, T. Szemberg and H. Tutaj-Gasińska, Symbolic powers of planar point configurations II, J. Pure Appl. Alg. 220 (2016) 2001–2016] to higher-dimensional projective spaces and classify all configurations of [Formula: see text]-planes [Formula: see text] in [Formula: see text] with the Waldschmidt constants less than two. We also determine some numerical and algebraic invariants of the defining ideals [Formula: see text] of these classes of configurations, i.e. the resurgence, the minimal free resolution and the regularity of [Formula: see text], as well as the Hilbert function of [Formula: see text].

THE PROJECTIVE DIMENSION OF THE EDGE IDEAL OF A VERY WELL-COVERED GRAPH

2017 ◽  
Vol 230 ◽  
pp. 160-179 ◽  
Author(s):  
KYOUKO KIMURA ◽  
NAOKI TERAI ◽  
SIAMAK YASSEMI
Keyword(s):  
Projective Dimension ◽  
Free Resolution ◽  
Covering Number ◽  
Edge Ideal ◽  
Minimal Free Resolution ◽  
Symbolic Powers

A very well-covered graph is an unmixed graph whose covering number is half of the number of vertices. We construct an explicit minimal free resolution of the cover ideal of a Cohen–Macaulay very well-covered graph. Using this resolution, we characterize the projective dimension of the edge ideal of a very well-covered graph in terms of a pairwise$3$-disjoint set of complete bipartite subgraphs of the graph. We also show nondecreasing property of the projective dimension of symbolic powers of the edge ideal of a very well-covered graph with respect to the exponents.

scholarly journals Gluing semigroups and strongly indispensable free resolutions

2019 ◽  
Vol 29 (02) ◽  
pp. 263-278
Author(s):  
Mesut Şahi̇n ◽  
Leah Gold Stella
Keyword(s):  
Complete Intersection ◽  
Special Property ◽  
Free Resolution ◽  
Numerical Semigroups ◽  
Free Resolutions ◽  
Semigroup Rings ◽  
Minimal Free Resolution ◽  
Minimal Free Resolutions ◽  
Symmetric Numerical Semigroups

We study strong indispensability of minimal free resolutions of semigroup rings focusing on the operation of gluing used in the literature to take examples with a special property and produce new ones. We give a naive condition to determine whether gluing of two semigroup rings has a strongly indispensable minimal free resolution. As applications, we determine simple gluings of [Formula: see text]-generated non-symmetric, [Formula: see text]-generated symmetric and pseudo symmetric numerical semigroups as well as obtain infinitely many new complete intersection semigroups of any embedding dimensions, having strongly indispensable minimal free resolutions.

scholarly journals Curves with Two Pencils and Associated Maps to Projective Spaces

2006 ◽  
Vol 13 (3) ◽  
pp. 411-417
Author(s):  
Edoardo Ballico
Keyword(s):  
Linear System ◽  
Projective Spaces ◽  
Free Resolution ◽  
Homogeneous Ideal ◽  
Projective Curve ◽  
Minimal Free Resolution ◽  
Complete Linear System

Abstract Let 𝑋 be a smooth and connected projective curve. Assume the existence of spanned 𝐿 ∈ Pic𝑎(𝑋), 𝑅 ∈ Pic𝑏(𝑋) such that ℎ0(𝑋, 𝐿) = ℎ0(𝑋, 𝑅) = 2 and the induced map ϕ 𝐿,𝑅 : 𝑋 → 𝐏1 × 𝐏1 is birational onto its image. Here we study the following question. What can be said about the morphisms β : 𝑋 → 𝐏𝑅 induced by a complete linear system |𝐿⊗𝑢⊗𝑅⊗𝑣| for some positive 𝑢, 𝑣? We study the homogeneous ideal and the minimal free resolution of the curve β(𝑋).

scholarly journals Complete intersections primitive structures on space curves

2015 ◽  
Vol 26 (12) ◽  
pp. 1550104
Author(s):  
Philippe Ellia
Keyword(s):  
Complete Intersection ◽  
Smooth Surface ◽  
Smooth Curve ◽  
Complete Intersections ◽  
Multiple Structure ◽  
Space Curves ◽  
Structure Formula ◽  
Primitive Structure

A multiple structure [Formula: see text] on a smooth curve [Formula: see text] is said to be primitive if [Formula: see text] is locally contained in a smooth surface. We give some numerical conditions for a curve [Formula: see text] to be a primitive set theoretical complete intersection (i.e. to have a primitive structure which is a complete intersection).

scholarly journals Vector bundles of finite rank on complete intersections of finite codimension in ind-Grassmannians

2015 ◽  
Vol 2 (1) ◽  
Author(s):  
Svetlana Ermakova
Keyword(s):  
Vector Bundle ◽  
Complete Intersection ◽  
Finite Rank ◽  
Vector Bundles ◽  
Complete Intersections ◽  
Finite Codimension ◽  
Line Bundles ◽  
Direct Sum ◽  
Rank Vector

AbstractIn this article we establish an analogue of the Barth-Van de Ven-Tyurin-Sato theorem.We prove that a finite rank vector bundle on a complete intersection of finite codimension in a linear ind-Grassmannian is isomorphic to a direct sum of line bundles.

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