scholarly journals The h -vectors of arithmetically Gorenstein sets of points on a general sextic surface inP3

2014 ◽  
Vol 403 ◽  
pp. 345-362 ◽  
Author(s):  
Megan Patnott
Keyword(s):  
Arithmetically Gorenstein

scholarly journals Arithmetically Gorenstein Calabi--Yau threefolds in $\mathbb{P}^7$

2016 ◽  
Vol 23 (0) ◽  
pp. 52-68
Author(s):  
Stephen Coughlan ◽  
Łukasz Gołębiowski ◽  
Grzegorz Kapustka ◽  
Michał Kapustka
Keyword(s):  
Arithmetically Gorenstein

scholarly journals Hilbert functions of irreducible arithmetically Gorenstein schemes

2004 ◽  
Vol 272 (1) ◽  
pp. 292-310 ◽  
Author(s):  
Nero Budur ◽  
Marta Casanellas ◽  
Elisa Gorla
Keyword(s):  
Hilbert Functions ◽  
Arithmetically Gorenstein

scholarly journals $${\mathfrak {S}}_5$$-equivariant syzygies for the Del Pezzo surface of degree 5

2020 ◽  
Author(s):  
Ingrid Bauer ◽  
Fabrizio Catanese
Keyword(s):  
Automorphism Group ◽  
Symmetric Group ◽  
Blow Up ◽  
Pezzo Surface ◽  
Irreducible Representations ◽  
Del Pezzo Surface ◽  
Del Pezzo ◽  
Arithmetically Gorenstein ◽  
Pfaffian Equations

Abstract The Del Pezzo surface Y of degree 5 is the blow up of the plane in 4 general points, embedded in $${\mathbb {P}}^5$$P5 by the system of cubics passing through these points. It is the simplest example of the Buchsbaum–Eisenbud theorem on arithmetically-Gorenstein subvarieties of codimension 3 being Pfaffian. Its automorphism group is the symmetric group $${\mathfrak {S}}_5$$S5. We give canonical explicit $${\mathfrak {S}}_5$$S5-invariant Pfaffian equations through a 6$$\times $$×6 antisymmetric matrix. We give concrete geometric descriptions of the irreducible representations of $${\mathfrak {S}}_5$$S5. Finally, we give $${\mathfrak {S}}_5$$S5-invariant equations for the embedding of Y inside $$({\mathbb {P}}^1)^5$$(P1)5, and show that they have the same Hilbert resolution as for the Del Pezzo of degree 4.

The lazarsfeld-rao property on an arithmetically gorenstein variety

1993 ◽  
Vol 78 (1) ◽  
pp. 347-368 ◽  
Author(s):  
Giorgio Bolondi ◽  
Juan Carlos Migliore
Keyword(s):  
Arithmetically Gorenstein ◽  
Gorenstein Variety

scholarly journals Codimension 3 Arithmetically Gorenstein Subschemes of projective N-space

2008 ◽  
Vol 58 (6) ◽  
pp. 2037-2073 ◽  
Author(s):  
Robin Hartshorne ◽  
Irene Sabadini ◽  
Enrico Schlesinger
Keyword(s):  
Arithmetically Gorenstein

On Complete Intersections Contained in Cohen-Macaulay and Gorenstein Ideals

2011 ◽  
Vol 18 (spec01) ◽  
pp. 857-872 ◽  
Author(s):  
Alfio Ragusa ◽  
Giuseppe Zappalà
Keyword(s):  
Minimal Element ◽  
Complete Intersections ◽  
Arithmetically Gorenstein

We look for complete intersections containing certain arithmetically Cohen-Macaulay schemes, and give a complete description in the case of 2-codimensional arithmetically Cohen-Macaulay schemes and 3-codimensional arithmetically Gorenstein schemes. In particular, we prove that in these cases the sets of types of complete intersections containing such schemes have a unique minimal element and we compute it.

scholarly journals Wahl maps and extensions of canonical curves and K⁢3K3 surfaces

2020 ◽  
Vol 2020 (761) ◽  
pp. 219-245
Author(s):  
Ciro Ciliberto ◽  
Thomas Dedieu ◽  
Edoardo Sernesi
Keyword(s):  
Projective Curve ◽  
Canonical Embedding ◽  
Linear Section ◽  
Smooth Projective Curve ◽  
Clifford Index ◽  
Normal Variety ◽  
Canonical Curves ◽  
Wahl Map ◽  
Arithmetically Gorenstein

AbstractLet C be a smooth projective curve (resp. {(S,L)} a polarized {K3} surface) of genus {g\geqslant 11}, with Clifford index at least 3, considered in its canonical embedding in {\mathbb{P}^{g-1}} (resp. in its embedding in {|L|^{\vee}\cong\mathbb{P}^{g}}). We prove that C (resp. S) is a linear section of an arithmetically Gorenstein normal variety Y in {\mathbb{P}^{g+r}}, not a cone, with {\dim(Y)=r+2} and {\omega_{Y}=\mathcal{O}_{Y}(-r)}, if the cokernel of the Gauss–Wahl map of C (resp. {\operatorname{H}^{1}(T_{S}\otimes L^{\vee})}) has dimension larger than or equal to {r+1} (resp. r). This relies on previous work of Wahl and Arbarello–Bruno–Sernesi. We provide various applications.

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