For a one-parameter degeneration of reduced compact complex analytic spaces dimension $n$, we prove the invariance frontier Hodge numbers $h^{p,q}$ (that is, with $pq(n-p)(n-q)=0$) for intersection cohomology fibers and also their desingularizations, assuming that central fiber is reduced, projective, has only rational singularities. This can be shown to equivalent structure sheaf (which known ...

Dualizing marked Petri nets results in tokens for transitions (t-tokens). A marked transition can strictly not be enabled, even if there are sufficient ”enabling” tokens (p-tokens) on its input places. On the other hand, t-tokens can be moved by the firing of places. This permits flows of t-tokens which describe sequences of non-events. Their benefit to simulation is the possibility to model (a...

We give a close formula for the N\'eron-Tate height of tautological integral cycles on Jacobians curves over number fields as well new lower bound arithmetic self-intersection $\hat{\omega}^2$ dualizing sheaf curve in terms Zhang's invariant $\varphi$. As an application, we obtain effective Bogomolov-type result cycles. deduce these results from more general combinatorial computation intersecti...

The Gorenstein projective modules are proved to form a precovering class in the module category of a ring which has a dualizing complex. 0. Introduction This paper proves over a wide class of rings that the Gorenstein projective modules form a precovering class in the module category. Let me explain this statement. There are two terms of mystery, “Gorenstein projective modules” and “precovering...

Several results about the multiplicities of indecomposable injectives in the minimal injective resolution of a ring exist in the literature. Mostly these apply to universal enveloping algebras of finite dimensional solvable Lie algebras, and to Gorenstein noetherian PI local rings. We unify these results and extend them to the much wider class of rings with Auslander dualizing complexes.

We combine a Lagrangian approach inspired by convex and quasiconvex dualities with a penalization approach to mathematical programming. We use the ideas of abstract convexity. We focus our attention on the set of multipliers. We look for an interpretation of multipliers as elements of generalized subdifferentials of the performance function associated with a dualizing parameterization of the gi...

The parabolic Kazhdan–Lusztig polynomials for Grassmannians can be computed by counting Dyck partitions. We “lift” this combinatorial formula to the corresponding category of singular Soergel bimodules obtain bases Hom spaces between indecomposable objects. In particular, we describe intersection cohomology Schubert varieties in parametrized partitions which extend (after dualizing) classical b...