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Fano varieties with large Seshadri constants in positive characteristic
TLDR
In this paper, the Seshadri constant of the anti-canonical divisor at some smooth point is shown to be greater than a constant in the dimension of a Fano variety.Abstract:
We prove that a Fano variety (with arbitrary singularities) of dimension $n$ in positive characteristic is isomorphic to $\mathbb{P}^n$ if the Seshadri constant of the anti-canonical divisor at some smooth point is greater than $n$ and classify Fano varieties whose anti-canonical divisors have Seshadri constants $n$. In characteristic $p>5$ and dimension $3$, we also show that Fano varieties $X$ with Seshadri constants $\epsilon(-K_X,x)>2+\epsilon$ at some smooth point $x\in X$ (for some fixed $\epsilon>0$) have bounded anti-canonical degrees.read more
Citations
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Seshadri constants for vector bundles
TL;DR: In this paper, Seshadri constants for line bundles in a relative setting were introduced and used to control separation of jets for direct images of pluricanonical bundles, in the spirit of a relative Fujita-type conjecture of Popa and Schnell.
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Seshadri Constants and Fujita's Conjecture via Positive Characteristic Methods
TL;DR: In this paper, a new approach to prove Fujita's conjecture using Seshadri constants and positive characteristic methods was presented, which was proved in characteristic zero by Bauer and Szemberg.
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Seshadri constants for vector bundles
TL;DR: In this paper, the authors introduce Seshadri constants for line bundles in a relative setting, which generalize the classical Seshadi constants of line bundles on projective varieties and their extension to vector bundles studied by Beltrametti-Schneider Sommese and Hacon.
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Weak boundedness of Fano threefolds with large Seshadri constants in characteristic $p>5$
TL;DR: In this paper, it was shown that the anticanonical volume of a Fano threefold with arbitrary singularities has Seshadri constant at some smooth point in the Fano.
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On the boundedness of globally F-split varieties
TL;DR: In this paper , the use of F -split and globally F -regular conditions in the pursuit of BAB type results in positive characteristic was proposed, and the main technical work comes in the form of a detailed study of threefold Mori fibre spaces over positive dimensional bases.
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TL;DR: In this article, the authors present conditions générales d'utilisation (http://www.numdam.org/conditions), i.e., Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.