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EXERCISES IN THE BIRATIONAL GEOMETRY OF ALGEBRAIC VARIETIES
, 2008
"... The book [KM98] gave an introduction to the birational geometry of algebraic varieties, as the subject stood in 1998. The developments of the last decade made the more advanced parts of Chapters 6 and 7 less important and the detailed treatment of surface singularities in Chapter 4 less necessary. H ..."
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Cited by 322 (1 self)
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The book [KM98] gave an introduction to the birational geometry of algebraic varieties, as the subject stood in 1998. The developments of the last decade made the more advanced parts of Chapters 6 and 7 less important and the detailed treatment of surface singularities in Chapter 4 less necessary
SEMIORTHOGONAL DECOMPOSITIONS FOR ALGEBRAIC VARIETIES
, 1995
"... A criterion for a functor between derived categories of coherent sheaves to be full and faithful is given. A semiorthogonal decomposition for the derived category of coherent sheaves on the intersection of two even dimensional quadrics is obtained. The behaviour of derived categories with respect to ..."
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Cited by 183 (11 self)
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to birational transformations is investigated. A theorem about reconstruction of a variety from the
algebraic varieties
"... Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at ..."
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Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at
On triangular decompositions of algebraic varieties
 Presented at the MEGA2000 Conference
, 1999
"... We propose an efficient algorithm for computing triangular decompositions of algebraic varieties. It is based on an incremental process and produces components in order of decreasing dimension. The combination of these two major features is obtained by means of lazy evaluation techniques and a lifti ..."
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Cited by 75 (34 self)
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We propose an efficient algorithm for computing triangular decompositions of algebraic varieties. It is based on an incremental process and produces components in order of decreasing dimension. The combination of these two major features is obtained by means of lazy evaluation techniques and a
Euler characteristics of algebraic varieties
 Communications on Pure and Applied Math. LXI
"... Abstract. The aim of this note is to study the behavior of intersection homology Euler characteristic under morphisms of algebraic varieties. The main result is a direct application of the BBDG decomposition theorem. Similar formulae for Hodgetheoretic invariants of algebraic varieties were announc ..."
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Cited by 18 (8 self)
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Abstract. The aim of this note is to study the behavior of intersection homology Euler characteristic under morphisms of algebraic varieties. The main result is a direct application of the BBDG decomposition theorem. Similar formulae for Hodgetheoretic invariants of algebraic varieties were
Geometry on Arc Spaces of Algebraic Varieties
 Proceedings of the Third European Congress of Mathematics, Barcelona 2000, Progr. Math. 201 (2001
, 2001
"... This paper is a survey on arc spaces, a recent topic in algebraic geometry and singularity theory. The geometry of the arc space of an algebraic variety yields several new geometric invariants and brings new light to some classical invariants. ..."
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Cited by 104 (7 self)
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This paper is a survey on arc spaces, a recent topic in algebraic geometry and singularity theory. The geometry of the arc space of an algebraic variety yields several new geometric invariants and brings new light to some classical invariants.
SINGULARITIES ON COMPLETE ALGEBRAIC VARIETIES
"... It is a classical question in algebraic geometry to understand what are the constraints imposed on the singularities that can be afforded on a given class of algebraic varieties. A general result in this direction appeared in [CG]. There it was shown that for any algebraic family of algebraic variet ..."
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It is a classical question in algebraic geometry to understand what are the constraints imposed on the singularities that can be afforded on a given class of algebraic varieties. A general result in this direction appeared in [CG]. There it was shown that for any algebraic family of algebraic
Germs of Arcs on Singular Algebraic Varieties and Motivic Integration
, 1999
"... Introduction Let k be a field of characteristic zero. We denote by M the Grothendieck ring of algebraic varieties over k (i.e. reduced separated schemes of finite type over k). It is the ring generated by symbols [S], for S an algebraic variety over k, with the relations [S] = [S 0 ] if S is iso ..."
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Cited by 183 (22 self)
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Introduction Let k be a field of characteristic zero. We denote by M the Grothendieck ring of algebraic varieties over k (i.e. reduced separated schemes of finite type over k). It is the ring generated by symbols [S], for S an algebraic variety over k, with the relations [S] = [S 0
Results 1  10
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5,803