Bogomolov inequality

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August undefined, 2024

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On the Bogomolov-Gieseker inequality in positive characteristic

WebSep 22, 2024 · We prove a version of the Bogomolov–Gieseker (BG) inequality on smooth projective surfaces of general type in positive characteristic. Our result is stronger than a … WebThe inequality is known to be sharp for some varieties (e.g. Abelian varieties), as well as non-sharp for some others (e.g. the projective plane). Besides Fano and K3 surfaces, it is always difficult to get stronger Bogomolov type inequalities for other surfaces and higher dimensional varieties. ffx farm spheres

The Bogomolov–Miyaoka–Yau inequality for logarithmic surfaces …

WebOct 30, 2001 · Bogomolov [1, Theorem 5] proved that c 2 1 [les ] 4 c 2. This was improved to c 2 1 [les ] 3 c 2 by Miyaoka [ 12 , Theorem 4] and Yau [ 19 , Theorem 4]. Equality c 2 1 [les ] 3 c 2 is attained, for example, if the universal cover of X is a ball (if κ( X ) = 2 then this is the only possibility). WebMar 1, 1999 · The main result is a Bogomolov-Miyaoka-Yau-type inequality which implies that if $(X,B)$ has log canonical singularities and $\kappa(X,K_X+B)\ge 0$ then … WebAug 22, 2024 · Download PDF Abstract: We prove a version of the Bogomolov-Gieseker inequality on smooth projective surfaces of general type in positive characteristic, which is stronger than the result by Langer when the ranks of vector bundles are sufficiently large. Our inequality enables us to construct Bridgeland stability conditions with full support … density of green heart

A generalized Bogomolov–Gieseker inequality for the three …

The inequality is false in positive characteristic: William E. Lang and Robert W. Easton gave examples of surfaces in characteristic p, such as generalized Raynaud surfaces, for which it fails. Formulation of the inequality. The conventional formulation of the Bogomolov–Miyaoka–Yau inequality is as follows. See more In mathematics, the Bogomolov–Miyaoka–Yau inequality is the inequality $${\displaystyle c_{1}^{2}\leq 3c_{2}}$$ between Chern numbers of compact complex surfaces See more If X is a surface of general type with $${\displaystyle c_{1}^{2}=3c_{2}}$$, so that equality holds in the Bogomolov–Miyaoka–Yau … See more The conventional formulation of the Bogomolov–Miyaoka–Yau inequality is as follows. Let X be a compact complex surface of general type, and let c1 = c1(X) and c2 = c2(X) be the first and second Chern class of the complex tangent bundle of the surface. Then See more WebIn mathematics, the Bogomolov–Miyaoka–Yau inequality is the inequality. between Chern numbers of compact complex surfaces of general type.Its major interest is the way it restricts the possible topological types of the underlying real 4-manifold. It was proved independently by S.-T. Yau (1977, 1978) and Yoichi Miyaoka (), after Van de Ven (1966) … ffx fiend arenaWebJul 19, 2024 · We prove Bogomolov's inequality for semistable sheaves on product type varieties in arbitrary characteristic. This gives the first examples of varieties with positive … density of graphene

"WebWu-yen Chuang, Ching-Jui Lai. Mathematics. 2015. We prove a Bogomolov-Gieseker type inequality for the third Chern characters of stable sheaves on Calabi-Yau 3-folds and a large class of Fano 3-folds with given rank and first and second Chern…. Expand. " - Bogomolov inequality

Bogomolov inequality

Bogomolov–Miyaoka–Yau inequality - HandWiki

WebOct 1, 2016 · We generalize Bogomolov’s inequality for Higgs sheaves and the Bogomolov– Miyaoka–Yau inequality in positive characteristic to the logarithmic case. … WebBogomolov-Gieseker type inequality, which is due to A. Moriwaki. Proposition 1 ([Ml,Theorem 1]). Let X be a smooth projective variety of dimen-sion d > 2, and let H be an ample line bundle on X. Let E be a rank-two vector bundle on X which is p-semistable with respect to H. Then we have {cx(E)2-4c2(E)}.Hd~2<0. Let X, H be as above.

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WebA generalized Bogomolov–Gieseker inequality for tilt-stable complexes on a smooth projective threefold was conjectured by Bayer, Toda, and the author. We show that such inequality holds true in general if it holds true when the polarization is sufficiently small. As an application, we prove it for the three-dimensional projective space. WebA generalized Bogomolov–Gieseker inequality for the three-dimensional projective space, Algebra Number Theory. 8 (2014), 173 ...

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WebMar 1, 1999 · The main result is a Bogomolov-Miyaoka-Yau-type inequality which implies that if $(X,B)$ has log canonical singularities and $\kappa(X,K_X+B)\ge 0$ then $(K_X+B)^2\le 3e_{\rm orb}(X,B)$. The actual inequality proved is somewhat stronger and it also implies all the previously published versions of the Bogomolov-Miyaoka-Yau …

WebThe orbifold version of the Bogomolov{Miyaoka{Yau inequality is the following, developed in the series of papers [Sak80, Miy84, KNS89, Meg92]. Theorem 1. Let S be a normal projective surface with quotient singularities such that ¡c1(S) is ample (or at least nef). Then c1(S)2 • 3eorb(S): (1:1) density of greenheart timberWebWe construct two infinite families of ball quotient compactifications birational to bielliptic surfaces. For each family, the volume spectrum of the associated noncompact finite volume ball quotient surfaces is the set… density of gravel in kg/m3WebOct 1, 2016 · We generalize Bogomolov’s inequality for Higgs sheaves and the Bogomolov– Miyaoka–Yau inequality in positive characteristic to the logarithmic case. We also generalize Shepherd-Barron’s results on Bogomolov’s inequality on surfaces of special type from rank 2 to the higher-rank case. We use these results to show some … ffx farming winning formulaWebThe book includes such fundamental results as arithmetic Hilbert–Samuel formula, arithmetic Nakai–Moishezon criterion, arithmetic Bogomolov inequality, the existence of small sections, the continuity of arithmetic volume function, the Lang–Bogomolov conjecture and so on. ff x ff crossWebAbstract. We prove Bogomolov’s inequality for Higgs sheaves on varieties in positive characteristic (Formula presented.) that can be lifted modulo (Formula presented.). This … density of graphite kg/m3WebAugust, 2024 On the Bogomolov-Miyaoka-Yau Inequality for Stacky Surfaces. Jiun-Cheng Chen, Hsian-Hua Tseng. Taiwanese J. Math. 24(4): 841-853 (August, 2024). DOI: 10.11650/tjm/190802. ABOUT FIRST PAGE CITED BY REFERENCES DOWNLOAD PAPER SAVE TO MY LIBRARY ... density of green douglas firWebMar 24, 2024 · Bogomolov-Miyaoka-Yau Inequality Relates invariants of a curve defined over the integers . If this inequality were proven true, then Fermat's last theorem would … ffx finaland