Related papers: Note on holomorphic Morse inequalities tensoring w…
In this paper, we establish strong holomorphic Morse inequalities on non-compact manifolds under the condition of optimal fundamental estimates. We show that optimal fundamental estimates are satisfied and then strong holomorphic Morse…
We prove the equivariant holomorphic Morse inequalities for a holomorphic torus action on a holomorphic vector bundle over a compact Kahler manifold when the fixed-point set is not necessarily discrete. Such inequalities bound the twisted…
Sheaves and sheaf cohomology are powerful tools in computational topology, greatly generalizing persistent homology. We develop an algorithm for simplifying the computation of cellular sheaf cohomology via (discrete) Morse-theoretic…
In this note we prove a weighted version of the Khintchine inequalities.
The paper aims to propose a suitable method in finding the solution of tensor complementarity problem. The tensor complementarity problem is a subclass of nonlinear complementarity problems for which the involved function is defined by a…
Consider a holomorphic torus action on vector bundles over a complex manifold which lifts to a holomorphic vector bundle. When the connected components of the fixed-point set are partially ordered, we construct, using sheaf-theoretical…
The goal of this work is to study the existence and properties of non constant entire curves f drawn in a complex irreducible n-dimensional variety X, and more specifically to show that they must satisfy certain global algebraic or…
In this note, we derive non trivial sharp bounds related to the weighted harmonic-geometric-arithmetic means inequalities, when two out of the three terms are known. As application, we give an explicit bound for the trace of the inverse of…
We study asymptotic estimates of the dimension of cohomology on possibly non-compact complex manifolds for line bundles endowed with Hermitian metrics with algebraic singularities. We give a unified approach to establishing singular…
We review some convexity inequalities for Hermitian matrices an add one more to the list.
We consider coherent and cohesive sheaves of $\cO$--modules over open sets $\Omega\subset\bC^n$. We prove that coherent sheaves, and certain other sheaves derived from them, are cohesive; and conversely, certain sheaves derived from…
We provide detailed holomorphic Morse estimates for the cohomology of sheaves of jet differentials and their dual sheaves. These estimates apply on arbitrary directed varieties, and a special attention has been given to the analysis of the…
Consider an action of a connected compact Lie group on a compact complex manifold $M$, and two equivariant vector bundles $L$ and $E$ on $M$, with $L$ of rank 1. The purpose of this paper is to establish holomorphic Morse inequalities \`{a}…
In recent years several classes of structured matrices are extended to classes of tensors in the context of tensor complementarity problem. The tensor complementarity problem is a class of nonlinear complementarity problem where the…
We introduce Morse-type inequalities for a holomorphic circle action on a holomorphic vector bundle over a compact Kaehler manifold. Our inequalities produce bounds on the multiplicities of weights occurring in the twisted Dolbeault…
We describe an analogue of the notion of a perverse sheaf in the setting of the derived category of coherent sheaves on an algebraic stack. Under strong additional assumptions the construction of coherent "intersection cohomology" complexes…
In this note we use the divisorial Zariski decomposition to give a more intrinsic version of the algebraic Morse inequalities.
A correspondence between quasicoherent sheaves on toric schemes and graded modules over some homogeneous coordinate ring is presented, and the behaviour of several finiteness properties under this correspondence is investigated.
We give an exposition of the Horn inequalities and their triple role characterizing tensor product invariants, eigenvalues of sums of Hermitian matrices, and intersections of Schubert varieties. We follow Belkale's geometric method, but…
We survey old and new results on the existence of moduli spaces of semistable coherent sheaves both in algebraic and in complex geometry.