اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدThe set of jumping conics of a locally free sheaf of dimension 2 on $P^2$
312
0
0.0
(
0
)
تأليف
Dmitry Logachev
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We consider a locally free sheaf $F$ of dimension 2 on $P^2$. A conic $q$ on $P^2$ is called a jumping conic if the restriction of $F$ to $q$ is not the generic one. We prove that the set of jumping conics is the maximal determinantal variety of a skew form. Some properties of this skew form are found.
قيم البحث
اقرأ أيضاً
We prove a formula for Chow groups of $Quot$-schemes which resolve degeneracy loci of a map between vector bundles, under expected dimension conditions. This result provides a unified way to understand known formulae for various geometric situations
such as blowups, Cayleys trick, projectivizations, Grassmannian bundles, flops from Springer type resolutions, as well as provide new phenomena such as formulae for Grassmannain type flips/flops and virtual flips. We also give applications to blowups of determinantal ideals, moduli spaces of linear series on curves, and Hilbert schemes of points on surfaces.
We consider the rigid monoidal category of character sheaves on a smooth commutative group scheme $G$ over a finite field $k$ and expand the scope of the function-sheaf dictionary from connected commutative algebraic groups to this setting. We find t
he group of isomorphism classes of character sheaves on $G$ and show that it is an extension of the group of characters of $G(k)$ by a cohomology group determined by the component group scheme of $G$. We also classify all morphisms in the category character sheaves on $G$. As an application, we study character sheaves on Greenberg transforms of locally finite type Neron models of algebraic tori over local fields. This provides a geometrization of quasicharacters of $p$-adic tori.
For a scheme $X$ defined over the length $2$ $p$-typical Witt vectors $W_2(k)$ of a characteristic $p$ field, we introduce total $p$-differentials which interpolate between Frobenius-twisted differentials and Buiums $p$-differentials. They form a she
af over the reduction $X_0$, and behave as if they were the sheaf of differentials of $X$ over a deeper base below $W_2(k)$. This allows us to construct the analogues of Gauss-Manin connections and Kodaira-Spencer classes as in the Katz-Oda formalism. We make connections to Frobenius lifts, Borger-Weilands biring formalism, and Deligne--Illusie classes.
Computation of parallel lines (envelopes) to parabolas, ellipses, and hyperbolas is of importance in structure engineering and theory of mechanisms. Homogeneous polynomials that implicitly define parallel lines for the given offset to a conic are fou
nd by computing Groebner bases for an elimination ideal of a suitably defined affine variety. Singularity of the lines is discussed and their singular points are explicitly found as functions of the offset and the parameters of the conic. Critical values of the offset are linked to the maximum curvature of each conic. Application to a finite element analysis is shown. Keywords: Affine variety, elimination ideal, Groebner basis, homogeneous polynomial, singularity, family of curves, envelope, pitch curve, undercutting, cam surface
We describe new components of the Gieseker--Maruyama moduli scheme $mathcal{M}(n)$ of semistable rank 2 sheaves $E$ on $mathbb{P}^3$ with $c_1(E)=0$, $c_2(E)=n$ and $c_3(E)=0$ whose generic point corresponds to non locally free sheaves. We show that
such components grow in number as $n$ grows, and discuss how they intersect the instanton component. As an application, we prove that $mathcal{M}(2)$ is connected, and identify a connected subscheme of $mathcal{M}(3)$ consisting of 7 irreducible components.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
