57,427 research outputs found
On the Maximal Rank Conjecture for Line Bundles of Extremal Degree
We propose a new method, using deformation theory, to study the maximal rank
conjecture. For line bundles of extremal degree, which can be viewed as the
first case to test the conjecture, we prove that maximal rank conjecture holds
by our new method
Some results on the generic vanishing of Koszul cohomology via deformation theory
We study the deformation-obstruction theory of Koszul cohomology groups of
's on singular nodal curves. We compute the obstruction classes for
Koszul cohomology classes on singular curves to deform to a smooth one. In the
case the obstructions are nontrivial, we obtain some partial results for
generic vanishing of Koszul cohomology groups.Comment: 25 pages, to appear in Pacific J. Mat
Monomial Difference Ideals
In this paper, basic properties of monomial difference ideals are studied. We
prove the finitely generated property of well-mixed difference ideals generated
by monomials. Furthermore, a finite prime decomposition of radical well-mixed
monomial difference ideals is given. As a consequence, we prove that every
strictly ascending chain of radical well-mixed monomial difference ideals in a
difference polynomial ring is finite, which answers a question raised by E.
Hrushovski in the monomial case. Moreover, the Alexander Duality for monomial
ideals is generalized to the monomial case.Comment: 16 page
Difference Index of Quasi-Prime Difference Algebraic Systems
This paper is devoted to studying difference indices of quasi-prime
difference algebraic systems. We define the quasi dimension polynomial of a
quasi-prime difference algebraic system. Based on this, we give the definition
of the difference index of a quasi-prime difference algebraic system through a
family of pseudo-Jacobian matrices. Some properties of difference indices are
proved. In particular, an upper bound of difference indices is given. As
applications, an upper bound of the Hilbert-Levin regularity and an upper bound
of orders for difference ideal membership problem are deduced.Comment: 14 pages. arXiv admin note: substantial text overlap with
arXiv:1607.0407
Difference Index of Quasi-regular Difference Algebraic Systems
This paper is devoted to studying difference indices of quasi-regular
difference algebraic systems. We give the definition of difference indices
through a family of pseudo-Jacobian matrices. Some properties of difference
indices are proved. In particular, a Jacobi-type upper bound for the sum of the
order and the difference index is given. As applications, an upper bound of the
Hilbert-Levin regularity and an upper bound of the order for difference ideal
membership problem are deduced.Comment: 11 page
On Systems of Polynomials with At Least One Positive Real Zero
In this paper, we prove several theorems on systems of polynomials with at
least one positive real zero, which can be viewed as a partial generalization
of Birch's theorem. The method is based on the theory of conceive polynomials.
Moreover, a class of polynomials attaining their global minimums are given,
which is useful in polynomial optimization.Comment: 10 page
On Supports of Sums of Nonnegative Circuit Polynomials
In this paper, we prove that every SONC polynomial decomposes into a sum of
nonnegative circuit polynomials with the same support, which reveals the
advantage of SONC decompositions for certifying nonnegativity of sparse
polynomials compared with the classical SOS decompositions. By virtue of this
fact, we can decide SONC through relative entropy programming more
efficiently.Comment: 7 pages. arXiv admin note: substantial text overlap with
arXiv:1804.0945
A remark on the generic vanishing of Koszul cohomology
We give a sufficient condition to study the vanishing of certain Koszul
cohomology groups for general pairs by induction. As an
application, we show that to prove the Maximal Rank Conjecture (for quadrics),
it suffices to check all cases with the Brill-Noether number .Comment: 7 pages. Comments are welcom
Comment on "Piezoelectricity in planar boron nitride via a geometric phase"
Using the strain-dependent effective Hamiltonian and the geometric phase,
Droth et al. [Phys. Rev. B 94, 075404 (2016)] obtain an analytical expression
for the electronic contribution to the piezoelectricity of planar hexagonal
boron nitride (h -BN). Their analytical results of piezoelectric constants for
h -BN are invalid because of the mistakes in constructing the adiabatic process
of the piezoelectricity. In this comment, we reconstruct a proper adiabatic
process for piezoelectricity and formulate a general Berry phase expression for
the piezoelectric coefficients of two-dimensional piezoelectric crystals by
means of the modern theory of polarization. The corrected analytical results of
the piezoelectric constants are in complete consistency with the
first-principles calculations and hence manifest the validity and generality of
the Berry phase expression of piezoelectric coefficients
Layouts for Plane Graphs on Constant Number of Tracks
A \emph{-track} layout of a graph consists of a vertex colouring, and
a total order of each vertex colour class, such that between each pair of
colour classes no two edges cross. A \emph{-queue} layout of a graph
consists of a total order of the vertices, and a partition of the edges into
sets such that no two edges that are in the same set are nested with
respect to the vertex ordering. The \emph{track number} (\emph{queue number})
of a graph , is the minimum such that has a -track (-queue)
layout. This paper proves that every -vertex plane graph has constant-bound
track and queue numbers. The result implies that every plane has a 3D
crossing-free straight-line grid drawing in volume. The proof utilizes a
novel graph partition technique.Comment: arXiv admin note: text overlap with arXiv:1302.0304 by other author
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