We give a precise formulation of the modularity principle for the log canonical models Mg(α) := Proj ⊕ d≥0 H (Mg , bd(KMg +αδ)c). We define a new invariant of Gorenstein curve singularities with Gm-action which can be used to predict the critical α-value at which a singularity first arises in the modular interpretation of Mg(α). We compute these critical α-values for large classes of singularit...

After the structure theorem of Buchsbaum and Eisenbud [1] on Gorenstein ideals of codimension 3, much progress was made in this area from the algebraic point of view; in particular some characterizations of these ideals using h−vectors (Stanley [9]) and minimal resolutions (Diesel [3]) were given. On the other hand, the Liaison theory gives some tools to exploit, but, at the same time, it requi...

We give some experimental data of Gorenstein liaison, working with points in P and curves in P , to see how far the familiar situation of liaison, biliaison, and Rao modules of curves in P will extend to subvarieties of codimension 3 in higher P . AMS classification numbers: 14H50, 14M07

Article history: Received 26 March 2009 Available online 23 October 2010 Communicated by Efim Zelmanov MSC: 16E05 16E10

We develop a theory of G-dimension over local homomorphisms which encompasses the classical theory of G-dimension for finitely generated modules over local rings. As an application, we prove that a local ring R of characteristic p is Gorenstein if and only if it possesses a nonzero finitely generated module of finite projective dimension that has finite G-dimension when considered as an R-modul...

0. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268 1. χ-functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270 2. BPS rationality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 2.1. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 2.2. Remarks . . . . . . . . . . . . . . . . . . . . . ....

We give an equivalence between the derived category of a locally finitely presented category and the derived category of contravariant functors from its finitely presented subcategory to the category of abelian groups, in the spirit of Krause’s work [H. Krause, Approximations and adjoints in homotopy categories, Math. Ann. 353 (2012), 765–781]. Then we provide a criterion for the existence of r...