منابع مشابه
Arithmetic Fujita approximation
— We prove an arithmetic analogue of Fujita’s approximation theorem in Arakelov geometry, conjectured by Moriwaki, by using slope method and measures associated to R-filtrations. Résumé. — On démontre un analogue arithmétique du théorème d’approximation de Fujita en géométrie d’Arakelov — conjecturé par Moriwaki — par la méthode de pentes et les mesures associées aux R-filtrations.
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Let R = k[x1, . . . , xn] be a polynomial ring over a field k. We present a characterization of multigraded R-modules in terms of the minors of their presentation matrix. We describe explicitly the second syzygies of any multigraded R-module.
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We develop a multigraded variant of Castelnuovo-Mumford regularity. Motivated by toric geometry, we work with modules over a polynomial ring graded by a finitely generated abelian group. As in the standard graded case, our definition of multigraded regularity involves the vanishing of graded components of local cohomology. We establish the key properties of regularity: its connection with the m...
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We introduce the multigraded Hilbert scheme, which parametrizes all homogeneous ideals with fixed Hilbert function in a polynomial ring that is graded by any abelian group. Our construction is widely applicable, it provides explicit equations, and it allows us to prove a range of new results, including Bayer’s conjecture on equations defining Grothendieck’s classical Hilbert scheme and the cons...
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X -ray crystallography is one of the best tools to determine a molecule’s structure. But it’s not much use when your cherished compound is a greasy smear that resolutely fails to crystallize. In 2013, Makoto Fujita of the University of Tokyo unveiled a method that offered hope to researchers struggling with stubborn samples. It relies on a metal organic framework (MOF), a highly porous lattice ...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 2011
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.2011.251.331