scholarly journals On Free Resolution of Weyl Module and Zero Characteristic Resolution In The Case of Partition (8,7,3)

2018 ◽  
Vol 15 (4) ◽  
Keyword(s):  
Free Resolution ◽  
Weyl Module ◽  
Zero Characteristic

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).

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 A note on the subadditivity of Syzygies

2016 ◽  
Vol 16 (09) ◽  
pp. 1750177 ◽  
Author(s):  
Sabine El Khoury ◽  
Hema Srinivasan
Keyword(s):  
Free Resolution ◽  
Graded Algebra ◽  
Gorenstein Algebras

Let [Formula: see text] be a graded algebra with [Formula: see text] and [Formula: see text] being the minimal and maximal shifts in the minimal graded free resolution of [Formula: see text] at degree [Formula: see text]. We prove that [Formula: see text] for all [Formula: see text]. As a consequence, we show that for Gorenstein algebras of codimension [Formula: see text], the subadditivity of maximal shifts [Formula: see text] in the minimal graded free resolution holds for [Formula: see text], i.e. we show that [Formula: see text] for [Formula: see text].

scholarly journals An algebraically closed field

1968 ◽  
Vol 9 (2) ◽  
pp. 146-151 ◽  
Author(s):  
F. J. Rayner
Keyword(s):  
Positive Integer ◽  
Power Series ◽  
Formal Power Series ◽  
Characteristic Zero ◽  
Closed Field ◽  
Algebraically Closed Field ◽  
Zero Characteristic ◽  
Image Position ◽  
Formal Power ◽  
Puiseux Expansions

Letkbe any algebraically closed field, and denote byk((t)) the field of formal power series in one indeterminatetoverk. Letso thatKis the field of Puiseux expansions with coefficients ink(each element ofKis a formal power series intl/rfor some positive integerr). It is well-known thatKis algebraically closed if and only ifkis of characteristic zero [1, p. 61]. For examples relating to ramified extensions of fields with valuation [9, §6] it is useful to have a field analogous toKwhich is algebraically closed whenkhas non-zero characteristicp. In this paper, I prove that the setLof all formal power series of the form Σaitei(where (ei) is well-ordered,ei=mi|nprt,n∈ Ζ,mi∈ Ζ,ai∈k,ri∈ Ν) forms an algebraically closed field.

SLn, Orthogonality Relations and Transfer

2007 ◽  
Vol 59 (3) ◽  
pp. 449-464 ◽  
Author(s):  
Alexandru Ioan Badulescu
Keyword(s):  
Division Algebra ◽  
Local Field ◽  
Finite Dimension ◽  
Complex Conjugate ◽  
Orbital Integrals ◽  
Central Division ◽  
Zero Characteristic ◽  
Central Division Algebra ◽  
Orthogonality Relations ◽  
Square Integrable Representation

AbstractLet π be a square integrable representation of G′ = SLn(D), with D a central division algebra of finite dimension over a local field F of non-zero characteristic. We prove that, on the elliptic set, the character of π equals the complex conjugate of the orbital integral of one of the pseudocoefficients of π. We prove also the orthogonality relations for characters of square integrable representations of G′. We prove the stable transfer of orbital integrals between SLn(F) and its inner forms.

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