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The main purpose of this paper is twofold. We first analyze in detail the meaningful geometric aspect of the method introduced in [12], concerning families of irreducible, nodal curves on a smooth, projective threefold X. This analysis gives some geometric interpretations not investigated in [12] and highlights several interesting connections with families of other singular geometric objects related to X and to other varieties. Then we use this method to study analogous problems for families of...

Equivariant sheaves on toric varieties

Valery Lunts (1995)

Compositio Mathematica

Equivariant vector bundles on toric varieties and some problems of linear algebra

A. A. Klyachko (1990)

Banach Center Publications

Equivariant vector bundles over affine subsets of the projective line

Corrado De Concini, Fabio Fagnani (1995)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Ergänzung zu der Arbeit: Vektorbündel vom Rang 2 über dem n-dimensionalen komplex-projektiven Raum.

Hans Grauert, Gerhard Mülich (1976)

Manuscripta mathematica

Erratum to : Morphisms, line bundles and moduli spaces in real algebraic geometry

Jacek Bochnak, Wojciech Kucharz, Robert Silhol (2000)

Publications Mathématiques de l'IHÉS

Examples of abelian surfaces in P4.

H. Lange, K. Hulek (1985)

Journal für die reine und angewandte Mathematik

Examples of non-ample normal bundles

Norman Goldstein (1984)

Compositio Mathematica

Exceptional collections on isotropic Grassmannians

Alexander Kuznetsov, Alexander Polishchuk (2016)

Journal of the European Mathematical Society

We introduce a new construction of exceptional objects in the derived category of coherent sheaves on a compact homogeneous space of a semisimple algebraic group and show that it produces exceptional collections of the length equal to the rank of the Grothendieck group on homogeneous spaces of all classical groups.

Exemples de courbes de P3 à fibré normal semi-stable, stable.

Ph. Ellia (1983)

Mathematische Annalen

Existence de faisceaux réflexifs de rang deux sur $P^{3}$ à bonne cohomologie

André Hirschowitz (1987)

Publications Mathématiques de l'IHÉS

Existence of Rank 3 Vector Bundles with Given Chern Classes on Homogeneous Rational 3-Folds.

C. Banica, Justin Coanda (1985)

Manuscripta mathematica

Explicit cogenerators for the homotopy category of projective modules over a ring

Amnon Neeman (2011)

Annales scientifiques de l'École Normale Supérieure

Let $R$ be a ring. In two previous articles [12, 14] we studied the homotopy category $𝐊 (R - Proj)$ of projective $R$ -modules. We produced a set of generators for this category, proved that the category is $ℵ_{1}$ -compactly generated for any ring $R$ , and showed that it need not always be compactly generated, but is for sufficiently nice $R$ . We furthermore analyzed the inclusion $j_{!}^{} : 𝐊 (R - Proj) \to 𝐊 (R - Flat)$ and the orthogonal subcategory $𝒮 = {𝐊 (R - Proj)}^{⊥}$ . And we even showed that the inclusion $𝒮 \to 𝐊 (R - Flat)$ has a right adjoint; this forces some natural map to be an equivalence...

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