Related papers: Polarizations and Hook Partitions

In this paper we study compactifications of heterotic string theory on manifolds satisfying the ddbar-lemma. We consider the Strominger system description of the low energy supergravity to first order in alpha' and show that the moduli of…

Applying a linearization theorem due to J. Mujica, we study the ideals of bounded holomorphic mappings $\mathcal{H}^\infty\circ\mathcal{I}$ generated by composition with an operator ideal $\mathcal{I}$. The bounded-holomorphic dual ideal of…

We prove compatibility relations between mixed Hodge numbers of $k$-Du Bois fibers in flat projective families and versal deformations of isolated $k$-Du Bois singularities. These extend the notion of polarized relations in asymptotic Hodge…

We consider the class of polynomial optimization problems $\inf \{f(x):x\in K\}$ for which the quadratic module generated by the polynomials that define $K$ and the polynomial $c-f$ (for some scalar $c$) is Archimedean. For such problems,…

We show that low-rank adaptation of large-scale models suffers from a low stable rank that is well below the linear algebraic rank of the subspace, degrading fine-tuning performance. To mitigate the underutilization of the allocated…

We study Stanley-Reisner ideals of broken circuits complexes and characterize those ones admitting a linear resolution or being complete intersections. These results will then be used to characterize arrangements whose Orlik-Terao ideal has…

The moir\'e Hubbard model describes correlations in certain homobilayer twisted transition metal dichalcogenides. Using exact diagonalization and density matrix renormalization group methods, we find magnetic Mott insulating and metallic…

We extend in two ways the standard Karush-Kuhn-Tucker optimality conditions to problems with a convex objective, convex functional constraints, and the extra requirement that some of the variables must be integral. While the standard…

Looking at the finite \'etale congruence covers $X(p)$ of a complex algebraic variety $X$ equipped with a variation of integral polarized Hodge structures whose period map is quasi-finite, we show that both the minimal gonality among all…

We propose a new way to condition random trees, that is, condition random trees to have large maximal out-degree. Under this new conditioning, we show that conditioned critical Galton-Watson trees converge locally to size-biased trees with…

Using the concept of vector partition functions, we investigate the asymptotic behavior of graded Betti numbers of powers of homogeneous ideals in a polynomial ring over a field. Our main results state that if the polynomial ring is…

We associate a family of ideal sheaves to any Q-effective divisor on a complex manifold, called higher multiplier ideals, using the theory of mixed Hodge modules and V-filtrations. This family is indexed by two parameters, an integer…

We introduce a notion of harmonic chain for chain complexes over fields of positive characteristic. A list of conditions for when a Hodge decomposition theorem holds in this setting is given and we apply this theory to finite CW complexes.…

Let $T$ be a compact torus. We prove that, up to equivariant rational equivalence, the category of $T$-simply connected, $T$-finite type $T$-spaces with finitely many isotropy types is completely described by certain finite systems of…

We consider the polynomial ring in finitely many variables over an algebraically closed field of positive characteristic, and initiate the systematic study of ideals preserved by the action of the general linear group by changes of…

We introduce the notion of power lattices that unifies and extends the equicardinal geometric lattices, Cartesian products of subspace lattices, and multiset subset lattices, among several others. The notions of shellability for simplicial…

Lorea [11] and later Frank et al. [8] generalized graphic matroids to hypergraphic matroids. In [8], the authors introduced hypertrees as a generalization of spanning trees and proved a form of the theorem of Tutte [18] and Nash-Williams…

Ensuring that a PDE model is well-posed is a necessary precursor to any form of analysis, control, or numerical simulation. Although the Lumer-Phillips theorem provides necessary and sufficient conditions for well-posedness of dissipative…

Let M be a matroid representable over a (partial) field P and B a matrix representable over a sub-partial field P' of P. We say that B confines M to P' if, whenever a P-representation matrix A of M has a submatrix B, A is a scaled…

We present several new sufficient conditions for uniform boundedness of the reduced correlations and free energy of an abstract polymer system in a complex multidisc around zero fugacity. They resolve a discrepancy between two incomparable…