Results 11 to 20 of about 533 (46)
Homological and combinatorial aspects of virtually Cohen–Macaulay sheaves
Transactions of the London Mathematical Society, Volume 8, Issue 1, Page 413-434, December 2021., 2021 Abstract When studying a graded module M over the Cox ring of a smooth projective toric variety X, there are two standard types of resolutions commonly used to glean information: free resolutions of M and vector bundle resolutions of its sheafification. Each approach comes with its own challenges.
Christine Berkesch +3 more
wiley +1 more source
Cosine polynomials with few zeros
Bulletin of the London Mathematical Society, Volume 53, Issue 3, Page 877-892, June 2021., 2021 Abstract In a celebrated paper, Borwein, Erdélyi, Ferguson and Lockhart constructed cosine polynomials of the form fA(x)=∑a∈Acos(ax),with A⊆N, |A|=n and as few as n5/6+o(1) zeros in [0,2π], thereby disproving an old conjecture of Littlewood. Here we give a sharp analysis of their constructions and, as a result, prove that there exist examples with as ...
Tomas Juškevičius, Julian Sahasrabudhe
wiley +1 more source
Tropical Lagrangian hypersurfaces are unobstructed
Journal of Topology, Volume 13, Issue 4, Page 1409-1454, December 2020., 2020 Abstract We produce for each tropical hypersurface V(ϕ)⊂Q=Rn a Lagrangian L(ϕ)⊂(C∗)n whose moment map projection is a tropical amoeba of V(ϕ). When these Lagrangians are admissible in the Fukaya–Seidel category, we show that they are unobstructed objects of the Fukaya category, and mirror to sheaves supported on complex hypersurfaces in a toric mirror.
Jeffrey Hicks
wiley +1 more source
On chains of centered valuations
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 69, Page 4347-4362, 2003., 2003 We study chains of centered valuations of a domain A and chains of centered valuations of A [X1, …, Xn] corresponding to valuations of A. Finally, we make some applications to chains of valuations centered on the same ideal of A [X1, …, Xn] and extending the same valuation of A.
Rachid Chibloun
wiley +1 more source
The containment problem and a rational simplicial arrangement
, 2017 Since Dumnicki, Szemberg and Tutaj-Gasi\'nska gave in 2013 in [9] the first example of a set of points in the complex projective plane such that for its homogeneous ideal I the containment of the third symbolic power in the second ordinary power fails ...
Malara, G., Szpond, J.
core +1 more source
Reduction numbers and initial ideals
, 2002 The reduction number r(A) of a standard graded algebra A is the least integer k such that there exists a minimal reduction J of the homogeneous maximal ideal m of A such that Jm^k=m^{k+1}.
Conca, Aldo
core +1 more source
Weitzenböck Derivations and Classical Invariant Theory II: The Symbolic Method [PDF]
, 2011 2000 Mathematics Subject Classification: 13N15, 13A50, 13F20.An analogue of the symbolic method of classical invariant theory for a representation and manipulation of the elements of the kernel of Weitzenböck derivations is ...
Bedratyuk, Leonid
core
On the Waring problem for polynomial rings
, 2011 In this note we discuss an analog of the classical Waring problem for C[x_0, x_1,...,x_n]. Namely, we show that a general homogeneous polynomial p \in C[x_0,x_1,...,x_n] of degree divisible by k\ge 2 can be represented as a sum of at most k^n k-th powers
Fröberg, Ralf +2 more
core +2 more sources
On the Stanley depth of powers of some classes of monomial ideals
, 2016 Given arbitrary monomial ideals $I$ and $J$ in polynomial rings $A$ and $B$ over a field $K$, we investigate the Stanley depth of powers of the sum $I+J$, and their quotient rings, in $A\otimes_K B$ in terms of those of $I$ and $J$.
Cimpoeas, Mircea
core +1 more source
Relative rank and regularization
Forum of Mathematics, SigmaWe introduce a new concept of rank – relative rank associated to a filtered collection of polynomials. When the filtration is trivial, our relative rank coincides with Schmidt rank (also called strength).
Amichai Lampert, Tamar Ziegler
doaj +1 more source