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 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 Formal meromorphic functions and cohomology on an algebraic variety

1980 ◽  
Vol 77 ◽  
pp. 125-135 ◽  
Author(s):  
Robert Speiser
Keyword(s):  
Algebraic Variety ◽  
Meromorphic Functions ◽  
Closed Subscheme ◽  
Gorenstein Variety

Let X be a projective Gorenstein variety, Y ⊂ X a proper closed subscheme such that X is smooth at all points of Y, so that the formal completion of X along Y is regular.

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.

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 Stiefel–Whitney numbers for singular varieties

2011 ◽  
Vol 150 (2) ◽  
pp. 273-289
Author(s):  
CARL McTAGUE
Keyword(s):  
Vector Space ◽  
Upper Bound ◽  
Elliptic Genus ◽  
Singular Varieties ◽  
Whitney Numbers ◽  
Bordism Ring ◽  
Genus One ◽  
Gorenstein Variety

AbstractThis paper determines which Stiefel–Whitney numbers can be defined for singular varieties compatibly with small resolutions. First an upper bound is found by identifying theF2-vector space of Stiefel–Whitney numbers invariant under classical flops, equivalently by computing the quotient of the unoriented bordism ring by the total spaces ofRP3bundles. These Stiefel–Whitney numbers are then defined for any real projective normal Gorenstein variety and shown to be compatible with small resolutions whenever they exist. In light of Totaro's result [Tot00] equating the complex elliptic genus with complex bordism modulo flops, equivalently complex bordism modulo the total spaces of3bundles, these findings can be seen as hinting at a new elliptic genus, one for unoriented manifolds.

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