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Derived Categories of Quadric Fibrations and Intersections of Quadrics
, 2005
"... We construct a semiorthogonal decomposition of the derived category of coherent sheaves on a quadric fibration consisting of several copies of the derived category of the base of the fibration and the derived category of coherent sheaves of modules over the sheaf of even parts of the Clifford algeb ..."
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Cited by 51 (12 self)
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We construct a semiorthogonal decomposition of the derived category of coherent sheaves on a quadric fibration consisting of several copies of the derived category of the base of the fibration and the derived category of coherent sheaves of modules over the sheaf of even parts of the Clifford
FINITENESS THEOREMS FOR ALGEBRAIC CYCLES ON QUADRIC FIBRATIONS
, 809
"... Abstract. We obtain finiteness theorems for algebraic cycles of codimensions 3 and 4 on quadric fibrations over curves over perfect fields. 1. ..."
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Abstract. We obtain finiteness theorems for algebraic cycles of codimensions 3 and 4 on quadric fibrations over curves over perfect fields. 1.
FINITENESS THEOREMS FOR ALGEBRAIC CYCLES OF SMALL CODIMENSION ON QUADRIC FIBRATIONS OVER CURVES
, 809
"... Abstract. We obtain finiteness theorems for algebraic cycles of small codimension on quadric fibrations X over curves over perfect fields k. For example, if k is finitely generated over Q and the fibration has relative dimension at least 11, then CH i (X) is finitely generated for i ≤ 4. 1. Introduc ..."
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Abstract. We obtain finiteness theorems for algebraic cycles of small codimension on quadric fibrations X over curves over perfect fields k. For example, if k is finitely generated over Q and the fibration has relative dimension at least 11, then CH i (X) is finitely generated for i ≤ 4. 1
AMPLE VECTOR BUNDLES AND INTRINSIC QUADRIC FIBRATIONS OVER IRRATIONAL CURVES
"... Several approaches in studying geometry of higher dimensional projectivevarieties rely on investigation of existence of particular subvarieties. It is wellknow, for instance, that, if Z is a hyperplane section or more generally, aneffective ample divisor of a projective variety X, the geometric char ..."
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characteristics of Entrato in Redazione il 10 maggio 2000. 1991 Mathematics Subject Classi�cation: Primary 14J60; secondary 14J40.Key words and phrases. Ample vector bundle. Quadric �bration. Polarization. Cone ofcurves.The author is member of the GNSAGA of the Italian CNR.
Spaces of sections of quadric surface fibrations over curves
 In Compact moduli spaces and vector bundles, volume 564 of Contemp. Math
, 2012
"... Let k be a field of characteristic not equal to two, B a smooth projective curve of genus g(B) over k, and F its function field. A quadric hypersurface fibration is a flat projective morphism π: X → B such that each geometric fiber is a quadric hypersurface with at worst an isolated ..."
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Cited by 4 (2 self)
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Let k be a field of characteristic not equal to two, B a smooth projective curve of genus g(B) over k, and F its function field. A quadric hypersurface fibration is a flat projective morphism π: X → B such that each geometric fiber is a quadric hypersurface with at worst an isolated
Ample subvarieties and rationally connected fibrations
, 2008
"... Under some positivity assumptions, extension properties of rationally connected fibrations from a submanifold to its ambient variety are studied. Given a family of rational curves on a complex projective manifold X inducing a covering family on a submanifold Y with ample normal bundle in X, the ma ..."
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Cited by 2 (1 self)
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Under some positivity assumptions, extension properties of rationally connected fibrations from a submanifold to its ambient variety are studied. Given a family of rational curves on a complex projective manifold X inducing a covering family on a submanifold Y with ample normal bundle in X
ON THE DERIVED CATEGORIES OF DEGREE d HYPERSURFACE FIBRATIONS
"... Abstract. We provide descriptions of the derived categories of degree d hypersurface fibrations which generalize a result of Kuznetsov for quadric fibrations and give a relative version of a wellknown theorem of Orlov. Using a local generator and Morita theory, we reinterpret the resulting matrix ..."
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Abstract. We provide descriptions of the derived categories of degree d hypersurface fibrations which generalize a result of Kuznetsov for quadric fibrations and give a relative version of a wellknown theorem of Orlov. Using a local generator and Morita theory, we reinterpret the resulting
Fibrations in complete intersections of quadrics, Clifford algebras, derived categories and rationality problems
, 2012
"... ..."
Regular Hyperbolic Fibrations
 MR 2002f:51018 Zbl 0991.51006
"... A hyperbolic bration is a set of q 1 hyperbolic quadrics and two lines which together partition the points of PG(3; q). The classical example of a hyperbolic bration comes from a pencil of quadrics; however, several other families are now known. In this paper we begin the development of a gene ..."
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Cited by 5 (1 self)
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A hyperbolic bration is a set of q 1 hyperbolic quadrics and two lines which together partition the points of PG(3; q). The classical example of a hyperbolic bration comes from a pencil of quadrics; however, several other families are now known. In this paper we begin the development of a
Results 1  10
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1,544