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Titlebook: On the Geometry of Some Special Projective Varieties; Francesco Russo Book 2016 Springer International Publishing Switzerland 2016 14N05,1

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發(fā)表于 2025-3-21 17:44:23 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書目名稱On the Geometry of Some Special Projective Varieties
編輯Francesco Russo
視頻videohttp://file.papertrans.cn/702/701171/701171.mp4
概述Winner of the 2015 Book Prize of the Unione Matematica Italiana.Includes supplementary material:
叢書名稱Lecture Notes of the Unione Matematica Italiana
圖書封面Titlebook: On the Geometry of Some Special Projective Varieties;  Francesco Russo Book 2016 Springer International Publishing Switzerland 2016 14N05,1
描述.Providing an introduction?to both classical and modern techniques in projective algebraic geometry, this monograph treats the geometrical properties of varieties embedded in projective spaces,?their secant and tangent lines, the behavior of tangent linear spaces, the algebro-geometric and topological obstructions to their embedding into?smaller projective spaces, and the classification of extremal cases.?It also provides a solution of Hartshorne’s Conjecture on Complete Intersections for the class of quadratic manifolds and new short proofs of previously known results,?using the?modern tools of Mori Theory and of rationally connected manifolds..The new approach to some of the problems considered can be resumed in the principle that, instead of studying a special embedded manifold uniruled by lines, one passes to analyze the original geometrical property on the manifold of lines passing through a general point and contained in the manifold. Once thisembedded manifold, usually of lower codimension, is classified, one tries to reconstruct the original manifold, following a principle appearing also in other areas of geometry such as projective differential geometry or complex geometry
出版日期Book 2016
關(guān)鍵詞14N05,14M07,14M10,14M22,14E30,14J70,14E05; Secant varieties; Hartshorne Conjecture on Complete interse
版次1
doihttps://doi.org/10.1007/978-3-319-26765-4
isbn_softcover978-3-319-26764-7
isbn_ebook978-3-319-26765-4Series ISSN 1862-9113 Series E-ISSN 1862-9121
issn_series 1862-9113
copyrightSpringer International Publishing Switzerland 2016
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發(fā)表于 2025-3-21 21:39:31 | 只看該作者
Tangent Cones, Tangent Spaces, Tangent Stars: Secant, Tangent, Tangent Star and Dual Varieties of aes to the involved varieties. We end the chapter by recalling the definition of dual variety, its first properties, the definitions of Gauss maps and the relations with reflexivity. Some exercises are introduced to complement the material presented.
板凳
發(fā)表于 2025-3-22 00:23:07 | 只看該作者
1862-9113 l and modern techniques in projective algebraic geometry, this monograph treats the geometrical properties of varieties embedded in projective spaces,?their secant and tangent lines, the behavior of tangent linear spaces, the algebro-geometric and topological obstructions to their embedding into?sma
地板
發(fā)表于 2025-3-22 04:42:48 | 只看該作者
The Hilbert Scheme of Lines Contained in a Variety and Passing Through a General Point,, we show in an elementary way that a lot of homogeneous varieties admit only trivial extensions, that is, those obtained by taking the cone .(.,?. ) with ., by constructing explicitly the cone via the study of the singularities of the corresponding Hilbert schemes of lines through a general point of ..
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發(fā)表于 2025-3-22 10:13:45 | 只看該作者
Local Quadratic Entry Locus Manifolds and Conic Connected Manifolds,o (Compos. Math. 144:949–962, 2008) and of Ionescu and Russo (Math. Res. Lett. 21:1137–1154, 2014) on dual defective manifolds. In particular, an astonishing simple proof of the famous Landman Parity Theorem for dual defective manifolds appears as an application of the tools developed in Chap.?.
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發(fā)表于 2025-3-22 14:25:32 | 只看該作者
Hartshorne Conjectures and Severi Varieties,ng the variety ., which essentially follows the approach of Zak in (Tangents and Secants of Algebraic Varieties. Translations of Mathematical Monographs, vol. 127. American Mathematical Society, Providence, 1993).
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發(fā)表于 2025-3-22 20:06:25 | 只看該作者
Lecture Notes of the Unione Matematica Italianahttp://image.papertrans.cn/o/image/701171.jpg
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發(fā)表于 2025-3-22 22:12:19 | 只看該作者
https://doi.org/10.1007/978-3-319-26765-414N05,14M07,14M10,14M22,14E30,14J70,14E05; Secant varieties; Hartshorne Conjecture on Complete interse
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