اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدThe G-Hilbert scheme for 1/r(1,a,r-a)
102
0
0.0
(
0
)
تأليف
Oskar Kedzierski
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Following Craw, Maclagan, Thomas and Nakamuras work on Hilbert schemes for abelian groups, we give an explicit description of the G-Hilbert scheme for G equal to a cyclic group of order r, acting on C^3 with weights 1,a,r-a. We describe how the combinatorial properties of the fan of G-Hilbert scheme relates to the Euclidean algorithm.
قيم البحث
اقرأ أيضاً
We prove that existence of a k-rational point can be detected by the stable A^1-homotopy category of S^1-spectra, or even a rationalized variant of this category.
Fix a Calabi-Yau 3-fold $X$ satisfying the Bogomolov-Gieseker conjecture of Bayer-Macr`i-Toda, such as the quintic 3-fold. We express Joyces generalised DT invariants counting Gieseker semistable sheaves of any rank $r$ on $X$ in terms of those cou
nting sheaves of rank 1. By the MNOP conjecture they are therefore determined by the Gromov-Witten invariants of $X$.
The ErdH{o}s-Simonovits stability theorem states that for all epsilon >0 there exists alpha >0 such that if G is a K_{r+1}-free graph on n vertices with e(G) > ex(n,K_{r+1}) - alpha n^2, then one can remove epsilon n^2 edges from G to obtain an r-par
tite graph. Furedi gave a short proof that one can choose alpha=epsilon. We give a bound for the relationship of alpha and varepsilon which is asymptotically sharp as epsilon to 0.
In this paper we consider the Brill-Noether locus $W_{underline d}(C)$ of line bundles of multidegree $underline d$ of total degree $g-1$ having a nonzero section on a nodal reducible curve $C$ of genus $ggeq2$. We give an explicit description of the
irreducible components of $W_{underline d}(C)$ for a semistable multidegre $underline d$. As a consequence we show that, if two semistable multidegrees of total degre $g-1$ on a curve with no rational components differ by a twister, then the respective Brill-Noether loci have isomorphic components.
The Hilbert scheme $mathbf{Hilb}_{p(t)}^{n}$ parametrizes closed subschemes and families of closed subschemes in the projective space $mathbb{P}^n$ with a fixed Hilbert polynomial $p(t)$. It is classically realized as a closed subscheme of a Grassman
nian or a product of Grassmannians. In this paper we consider schemes over a field $k$ of characteristic zero and we present a new proof of the existence of the Hilbert scheme as a subscheme of the Grassmannian $mathbf{Gr}_{p(r)}^{N(r)}$, where $N(r)= h^0 (mathcal{O}_{mathbb{P}^n}(r))$. Moreover, we exhibit explicit equations defining it in the Plucker coordinates of the Plucker embedding of $mathbf{Gr}_{p(r)}^{N(r)}$. Our proof of existence does not need some of the classical tools used in previous proofs, as flattening stratifications and Gotzmanns Persistence Theorem. The degree of our equations is $text{deg} p(t)+2$, lower than the degree of the equations given by Iarrobino and Kleiman in 1999 and also lower (except for the case of hypersurfaces) than the degree of those proved by Haiman and Sturmfels in 2004 after Bayers conjecture in 1982. The novelty of our approach mainly relies on the deeper attention to the intrinsic symmetries of the Hilbert scheme and on some results about Grassmannian based on the notion of extensors.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
