اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدOn the theory of Gordan-Noether on homogeneous forms with zero Hessian (Improved version)
44
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We give a detailed proof for Gordan-Noethers results in Ueber die algebraischen Formen, deren Hessesche Determinante identisch verschwindet published in 1876 in Mathematische Annahlen. C. Lossen has written a paper in a similar direction as the present paper, but did not provide a proof for every result. In our paper, every result is proved. Furthermore, our paper is independent of Lossens paper and includes a considerable number of new observations. An earlier version of this paper has been printed in Proceedings of the School of Science of Tokai University, Vol.49, Mar. 2014. In this version, a serious error has been corrected and some new results have been added.
قيم البحث
اقرأ أيضاً
Let $mathbb{K}$ be a field and $R = mathbb{K}[x_1, ldots, x_n]$. We obtain an improved upper bound for asymptotic resurgence of squarefree monomial ideals in $R$. We study the effect on the resurgence when sum, product and intersection of ideals are
taken. We obtain sharp upper and lower bounds for the resurgence and asymptotic resurgence of cover ideals of finite simple graphs in terms of associated combinatorial invariants. We also explicitly compute the resurgence and asymptotic resurgence of cover ideals of several classes of graphs. We characterize a graph being bipartite in terms of the resurgence and asymptotic resurgence of edge and cover ideals. We also compute explicitly the resurgence and asymptotic resurgence of edge ideals of some classes of graphs.
The purpose of this note is to introduce a multiplication on the set of homogeneous polynomials of fixed degree d, in a way to provide a duality theory between monomial ideals of K[x_1,ldots,x_d] generated in degrees leq n and block stable ideals (a
class of ideals containing the Borel fixed ones) of K[x_1,ldots,x_n] generated in degree d. As a byproduct we give a new proof of the characterization of Betti tables of ideals with linear resolution given by Murai.
In this paper, we introduce a new graph whose vertices are the nonzero zero-divisors of commutative ring $R$ and for distincts elements $x$ and $y$ in the set $Z(R)^{star}$ of the nonzero zero-divisors of $R$, $x$ and $y$ are adjacent if and only if
$xy=0$ or $x+yin Z(R)$. we present some properties and examples of this graph and we study his relation with the zero-divisor graph and with a subgraph of total graph of a commutative ring.
We continue our study of the new extension of zero-divisor graph. We give a complete characterization for the possible diameters of $widetilde{Gamma}(R)$ and $widetilde{Gamma}(R[x_1,dots,x_n])$, we investigate the relation between the zero-divisor gr
aph, the subgraph of total graph on $Z(R)^{star}$ and $widetilde{Gamma}(R)$ and we present some other properties of $widetilde{Gamma}(R)$.
Let $A$ be the polynomial algebra in $r$ variables with coefficients in an algebraically closed field $k$. When the characteristic of $k$ is $2$, Carlsson conjectured that for any $mathrm{dg}$-$A$-module $M$, which has dimension $N$ as a free $A$-mod
ule, if the homology of $M$ is nontrivial and finite dimensional as a $k$-vector space, then $Ngeq 2^r$. Here we examine a stronger conjecture concerning varieties of square-zero upper triangular $Ntimes N$ matrices with entries in $A$. Stratifying these varieties via Borel orbits, we show that the stronger conjecture holds when $N = 8$ without any restriction on the characteristic of $k$. This result also verifies that if $X$ is a product of $3$ spheres of any dimensions, then the elementary abelian $2$-group of order $4$ cannot act freely on $X$.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
