scholarly journals Derived equivalences and Serre duality for Gorenstein algebras

2009 ◽  
Vol 213 (11) ◽  
pp. 2156-2166
Author(s):  
Hiroki Abe ◽  
Mitsuo Hoshino
Keyword(s):  
Gorenstein Algebras ◽  
Derived Equivalences ◽  
Serre Duality

scholarly journals Derived equivalences and Gorenstein algebras

2007 ◽  
Vol 211 (1) ◽  
pp. 55-69 ◽  
Author(s):  
Hiroki Abe ◽  
Mitsuo Hoshino
Keyword(s):  
Gorenstein Algebras ◽  
Derived Equivalences

scholarly journals Higher-page Bott–Chern and Aeppli cohomologies and applications

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Dan Popovici ◽  
Jonas Stelzig ◽  
Luis Ugarte
Keyword(s):  
Positive Integer ◽  
Spectral Sequence ◽  
Complex Manifolds ◽  
Serre Duality ◽  
Frölicher Spectral Sequence ◽  
Compact Complex Manifolds

Abstract For every positive integer r, we introduce two new cohomologies, that we call E r {E_{r}} -Bott–Chern and E r {E_{r}} -Aeppli, on compact complex manifolds. When r = 1 {r\kern-1.0pt=\kern-1.0pt1} , they coincide with the usual Bott–Chern and Aeppli cohomologies, but they are coarser, respectively finer, than these when r ≥ 2 {r\geq 2} . They provide analogues in the Bott–Chern–Aeppli context of the E r {E_{r}} -cohomologies featuring in the Frölicher spectral sequence of the manifold. We apply these new cohomologies in several ways to characterise the notion of page- ( r - 1 ) {(r-1)} - ∂ ⁡ ∂ ¯ {\partial\bar{\partial}} -manifolds that we introduced very recently. We also prove analogues of the Serre duality for these higher-page Bott–Chern and Aeppli cohomologies and for the spaces featuring in the Frölicher spectral sequence. We obtain a further group of applications of our cohomologies to the study of Hermitian-symplectic and strongly Gauduchon metrics for which we show that they provide the natural cohomological framework.

scholarly journals Liftable derived equivalences and objective categories

2020 ◽  
Vol 52 (5) ◽  
pp. 816-834
Author(s):  
Xiaofa Chen ◽  
Xiao‐Wu Chen
Keyword(s):  
Derived Equivalences

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 Serre duality for rigid analytic spaces

1992 ◽  
Vol 3 (2) ◽  
pp. 219-235 ◽  
Author(s):  
Marius van der Put
Keyword(s):  
Serre Duality

scholarly journals Perverse Schobers and Wall Crossing

2017 ◽  
Vol 2019 (18) ◽  
pp. 5777-5810 ◽  
Author(s):  
W Donovan
Keyword(s):  
Invariant Theory ◽  
Local System ◽  
Vector Spaces ◽  
Geometric Invariant ◽  
Perverse Sheaf ◽  
Derived Equivalences ◽  
Grothendieck Groups ◽  
Wall Crossing ◽  
Git Quotient ◽  
Cohomology Complex

Abstract For a balanced wall crossing in geometric invariant theory (GIT), there exist derived equivalences between the corresponding GIT quotients if certain numerical conditions are satisfied. Given such a wall crossing, I construct a perverse sheaf of categories on a disk, singular at a point, with half-monodromies recovering these equivalences, and with behaviour at the singular point controlled by a GIT quotient stack associated to the wall. Taking complexified Grothendieck groups gives a perverse sheaf of vector spaces: I characterize when this is an intersection cohomology complex of a local system on the punctured disk.

Sign in / Sign up

Export Citation Format

Share Document