2 edition of **Intersecting cycles on an algebraic variety** found in the catalog.

Intersecting cycles on an algebraic variety

William Fulton

- 251 Want to read
- 15 Currently reading

Published
**1976**
by Aarhus Universitet, Matematisk Institut in Aarhus
.

Written in English

**Edition Notes**

Statement | [by]William Fulton and Robert MacPherson. |

Series | Preprint series -- 1976/77, No. 14. |

Contributions | MacPherson, Robert. |

The Physical Object | |
---|---|

Pagination | 34 p. |

Number of Pages | 34 |

ID Numbers | |

Open Library | OL21081847M |

This book is comprised of eight chapters and begins with a discussion on linear sections of an algebraic variety, with emphasis on the fibring of a variety defined over the complex numbers. The next two chapters focus on singular sections and hyperplane sections, focusing on . INTERSECTION THEORY 4 6. Properpushforward 0AZC Suppose that f: X →Y is a proper morphism of varieties. Let Z ⊂X be a k-dimensional closed deﬁne f ∗[Z] to be 0 if dim(f(Z)).

In mathematics, intersection theory is a branch of algebraic geometry, where subvarieties are intersected on an algebraic variety, and of algebraic topology, where intersections are computed within the cohomology ring. The theory for varieties is older, with roots in Bézout's theorem on curves and elimination theory. On the other hand, the. functions, sa y, semi-algebraic functions on an algebraic v ariet y (see [V2]). In this pap er, w e in tegrate f unctions which ta k e constan t v alues on the strata of S.

CYCLES IN AN ALGEBRAIC VARIETY (a) The absolute theory. If X is a cycle in V and if K is a field of definition for V, then a cycle X1 in V is said to be a specialization in V of X over K, if there exists a cycle X2 in S, whose components are either singular subvarieties in V or subvarieties in V - V, such that the cycle X1 + X2 is a. Ideal-variety correspondence The correspondence between algebra and geometry about to be discussed is the core of the area called algebraic geometry, which uses geometric intuition on one hand and algebraic formalism on the other. Computations in polynomial rings is what drives the e ective methods in algebraic geometry.

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On an algebraic variety. The theory of intersections of algebraic subvarieties and cycles. Let $ X $ be a smooth algebraic variety of dimension $ n $ over a field $ k $, while $ Y $ and $ Z $ are subvarieties of $ X $ of codimension $ i $ and $ j $, respectively.

If $ Y $ and $ Z $ intersect transversally, then $ Y \cap Z $ is a smooth subvariety of codimension $ i+ j $, which is denoted by. In mathematics, intersection theory is a branch of algebraic geometry, where subvarieties are intersected on an algebraic variety, and of algebraic topology, where intersections are computed within the cohomology theory for varieties is older, with roots in Bézout's theorem on curves and elimination the other hand, the topological theory more quickly reached a definitive form.

Intersection theory for cycles of an algebraic variety. Barsotti. Full-text: Open access. PDF File ( KB) DjVu File ( KB) Article info and citation C. Chevalley,Intersection of algebraic and algebroid varieties^ Trans.

Amer. Math. Soc. 57(), Cited by: 3. Whether you've loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for Intersecting cycles on an algebraic variety book.

1 Introduction to intersection theory in algebraic geometry. In mathematics, intersection theory is a branch of algebraic geometry, where subvarieties are intersected on an algebraic variety, and of algebraic topology, where intersections are computed within the cohomology ring.

The theory for varieties is older, with roots in Bézout's theorem on curves and elimination theory. On the other hand the. Products inK-theory and intersecting algebraic cycles. Daniel R. Grayson 1. In mathematics, an algebraic cycle on an algebraic variety V is a formal linear combination of subvarieties of are the part of the algebraic topology of V that is directly accessible by algebraic methods.

Understanding the algebraic cycles on a variety can give profound insights into the structure of the variety. The most trivial case is codimension zero cycles, which are linear. Algebraic Cycles Anand Sawant Abstract Algebraic cycles arose in the study of intersection theory for algebraic varieties.

This note, based on a a lecture in the Mathematics Students’ Seminar at TIFR on September 7, is meant to give an intorduction to algebraic cycles and various adequate equivalence relations on them. Fulton, W. and R., MacPherson, Intersecting cycles on an algebraic variety, Aarhus Universitet Preprint Series, no.

14 (). [Pp. in Real and complex singularities (Proc. Ninth Nordic Summer School/NAVF Sympos. Math., Oslo, ), Sijthoff and Noordhoff, Alphen aan den Rijn ().]. William Fulton and Robert MacPherson, Intersecting cycles on an algebraic variety, Real and complex singularities (Proc.

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on an algebraic variety. An element of the free Abelian group the set of free generators of which is constituted by all closed irreducible subvarieties of the given algebraic variety. The subgroup of the group $ C(X) $ of algebraic cycles on a variety $ X $ generated by a subvariety of codimension $ p $ is denoted by $ C ^ {p} (X) $.

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Lectures on algebraic cycles by Bloch: the references about algebraic cycles. An Invitation to Quantum Cohomology: Kontsevich's Formula for Rational Plane Curves by Kock and Vainsencher.

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Compatibility with intersection products, flat inverse image, and rational equivalence, modulo the coniveau filtration. Algebraic cycles. Let X d 2Var(k); let 0 i dand q= d i.

Let Z q(X) = Zi(X) be the group of algebraic cycles of dimension q(i.e. codi-mension i) on X1, i.e. the free abelian group generated by the k irreducible subvarieties Won Xof dimension q, but Wnot necessarily smooth. Therefore such and algebraic cycle Z2Z q(X) = Zi(X) can be written.Intersection theory: | | |Not to be confused with |Intersectionality theory|.| | | World Heritage Encyclopedia, the aggregation of the largest online.In algebraic geometry, the Chow groups (named after Wei-Liang Chow by Claude Chevalley ()) of an algebraic variety over any field are algebro-geometric analogs of the homology of a topological elements of the Chow group are formed out of subvarieties (so-called algebraic cycles) in a similar way to how simplicial or cellular homology groups are formed out of subcomplexes.