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1.
Recent work of Ein–Lazarsfeld–Smith and Hochster–Huneke raised the containment problem of determining which symbolic powers of an ideal are contained in a given ordinary power of the ideal. Bocci–Harbourne defined a quantity called the resurgence to address this problem for homogeneous ideals in polynomial rings, with a focus on zero-dimensional subschemes of projective space. Here we take the first steps toward extending this work to higher dimensional subschemes. We introduce new asymptotic versions of the resurgence and obtain upper and lower bounds on them for ideals I of smooth subschemes, generalizing what is done in Bocci and Harbourne (2010) [5]. We apply these bounds to ideals of unions of general lines in PN. We also pose a Nagata type conjecture for symbolic powers of ideals of lines in P3. 相似文献
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David L. Fearnley L. Fearnley J. W. Lamoreaux 《Proceedings of the American Mathematical Society》2003,131(7):2241-2245
This paper answers a question of Jan J. Dijkstra by giving a proof that all three-point sets are zero dimensional. It is known that all two-point sets are zero dimensional, and it is known that for all 3$">, there are -point sets which are not zero dimensional, so this paper answers the question for the last remaining case.
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Euisung Park 《Mathematische Nachrichten》2014,287(11-12):1383-1393
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Here we show the existence of strong restrictions for the Hilbert function of zerodimensional curvilinear subschemes of P
n
with one point as support and with high regularity index. 相似文献
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LetX be a locally compact non compact space. Necessary and sufficient conditions forfX/X to be a retract offX are given wherefX is the Freudenthal compactification ofX. LetX be a locally compact and zero dimensional space,m be any cardinal number andJ be a set with cardinalitym. It is proved thatX has a dyadic family of powerm if and only if there exist and compactificationY ofX such thatY/X=2 J andY/X is a retract ofY. 相似文献
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Edoardo Ballico Cristiano Bocci Claudio Fontanari 《Central European Journal of Mathematics》2004,2(4):538-560
Here we study zero-dimensional subschemes of ruled varieties, mainly Hirzebruch surfaces and rational normal scrolls, by applying
the Horace method and the Terracini method
This research is part of the T.A.S.C.A. project of I.N.d.A.M., supported by P.A.T. (Trento) and M.I.U.R. (Italy) 相似文献
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Let be a scroll over a smooth curve C and let denote the hyperplane bundle. The special geometry of X implies that certain sheaves related to the principal part bundles of are locally free. The inflectional loci of X can be expressed in terms of these sheaves, leading to explicit formulas for the cohomology classes of the loci. The formulas
imply that the only uninflected scrolls are the balanced rational normal scrolls.
相似文献
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P. L. N. Varma 《Mathematische Zeitschrift》1990,205(1):315-320
Senior Research Fellow of the Council of Scientific and Industrial Research, India. 相似文献
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Shiv Datt Kumar 《Archiv der Mathematik》2007,89(2):124-130
Let A be a commutative Noetherian ring and
be an ideal containing a monic polynomial such that A[T]/I is zero dimensional. Suppose the conormal module I/I
2 is generated by r elements over A[T]/I. Then a set of r generators of
can be lifted to a r generating set of I.
A part of this work is done at the Abdus Salam, International Centre for Theoretical Physics, Trieste, Italy.
Received: 12 March 2006 Revised: 29 January 2007 相似文献
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Osculating spaces of decomposable scrolls (of any genus and not necessarily normal) are studied and their inflectional loci are related to those of their generating curves by using systematically an idea introduced by Piene and Sacchiero in the setting of rational normal scrolls. In this broader setting the extra components of the second discriminant locus – deriving from flexes – are investigated and a new class of uninflected surface scrolls is presented and characterized. Further properties related to osculation are discussed for (not necessarily decomposable) scrolls (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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Joachim Jelisiejew Grzegorz Kapustka Micha Kapustka 《Mathematische Nachrichten》2019,292(9):2018-2027
We study the degrees of generators of the ideal of a projected Veronese variety to depending on the center of projection. This is related to the geometry of zero dimensional schemes of length 8 in , Cremona transforms of , and the geometry of Tonoli Calabi‐Yau threefolds of degree 17 in . 相似文献
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Daniel Levcovitz Israel Vainsencher Fernando Xavier 《Israel Journal of Mathematics》2007,161(1):103-123
We enumerate the cones over cubic scrolls satisfying appropriate incidence conditions to lines.
The first and second authors were partially supported by CNPq.
The third author was partially supported by PADCT/CNPq. 相似文献
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Edoardo Ballico 《Rendiconti del Circolo Matematico di Palermo》2008,57(2):173-179
Here we show that certain low rank ACM vector bundles on scrolls over smooth curves are iterated extensions of line bundles.
Partially supported by MIUR and GNSAGA of INDAM (Italy) 相似文献
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Alberto Calabri Ciro Ciliberto Flaminio Flamini Rick Miranda 《Rendiconti del Circolo Matematico di Palermo》2008,57(1):1-31
Abstract In this paper we study smooth, non-special scrolls S of degree d, genus g ≥ 0, with general moduli. In particular, we study the scheme of unisecant curves of a given degree on S. Our approach is mostly based on degeneration techniques.
Keywords Ruled surfaces, Hilbert schemes of scrolls, Moduli, Embedded degenerations
Mathematics Subject Classification (2000) 14J26, 14D06, 14C20, (Secondary) 14H60, 14N10 相似文献