scholarly journals An algebraic correspondence with applications to projective bundles and blowing up Chern classes

1975 ◽  
Vol 102 (1) ◽  
pp. 1-36 ◽  
Author(s):  
A. T. Lascu ◽  
D. B. Scott
Keyword(s):  
Chern Classes ◽  
Projective Bundles ◽  
Blowing Up ◽  
Algebraic Correspondence

scholarly journals Chern classes of blow-ups

2009 ◽  
Vol 148 (2) ◽  
pp. 227-242 ◽  
Author(s):  
PAOLO ALUFFI
Keyword(s):  
Normal Bundle ◽  
Blow Up ◽  
Explicit Computation ◽  
Chern Classes ◽  
Classical Formula ◽  
New Approach ◽  
Standard Argument ◽  
Singular Varieties ◽  
Blowing Up ◽  
Straightforward Computation

AbstractWe extend the classical formula of Porteous for blowing-up Chern classes to the case of blow-ups of possibly singular varieties along regularly embedded centers. The proof of this generalization is perhaps conceptually simpler than the standard argument for the nonsingular case, involving Riemann–Roch without denominators. The new approach relies on the explicit computation of an ideal, and a mild generalization of a well-known formula for the normal bundle of a proper transform ([8, B·6·10]).We also discuss alternative, very short proofs of the standard formula in some cases: an approach relying on the theory of Chern–Schwartz–MacPherson classes (working in characteristic 0), and an argument reducing the formula to a straightforward computation of Chern classes for sheaves of differential 1-forms with logarithmic poles (when the center of the blow-up is a complete intersection).

Blowing up Chern Classes

1960 ◽  
Vol 56 (2) ◽  
pp. 118-124 ◽  
Author(s):  
I. R. Porteous
Keyword(s):  
Algebraic Variety ◽  
Topological Structure ◽  
Chern Classes ◽  
Complete Proof ◽  
Blowing Up ◽  
Birational Transformation

The behaviour of the Chern classes or of the canonical classes of an algebraic variety under a dilatation has been studied by several authors (Todd (8)–(11), Segre (5), van de Ven (12)). This problem is of interest since a dilatation is the simplest form of birational transformation which does not preserve the underlying topological structure of the algebraic variety. A relation between the Chern classes of the variety obtained by dilatation of a subvariety and the Chern classes of the original variety has been conjectured by the authors cited above but a complete proof of this relation is not in the literature.

A Simple Proof of the Formula for the Blowing up of Chern Classes

1978 ◽  
Vol 100 (2) ◽  
pp. 293 ◽  
Author(s):  
A. T. Lascu ◽  
D. B. Scott
Keyword(s):  
Simple Proof ◽  
Chern Classes ◽  
Blowing Up

Constructing symplectic manifolds

2017 ◽  
Author(s):  
Dusa McDuff ◽  
Dietmar Salamon
Keyword(s):  
Final Section ◽  
Symplectic Manifolds ◽  
Homotopy Equivalence ◽  
Codimension Two ◽  
Open Manifolds ◽  
Connected Sums ◽  
Symplectic Forms ◽  
Ambient Manifold ◽  
Blowing Up ◽  
Four Manifolds

This chapter examines various ways to construct symplectic manifolds and submanifolds. It begins by studying blowing up and down in both the complex and the symplectic contexts. The next section is devoted to a discussion of fibre connected sums and describes Gompf’s construction of symplectic four-manifolds with arbitrary fundamental group. The chapter also contains an exposition of Gromov’s telescope construction, which shows that for open manifolds the h-principle rules and the inclusion of the space of symplectic forms into the space of nondegenerate 2-forms is a homotopy equivalence. The final section outlines Donaldson’s construction of codimension two symplectic submanifolds and explains the associated decompositions of the ambient manifold.

scholarly journals Numerical Criteria for Very Ampleness of Divisors on Projective Bundles Over an Elliptic Curve

1996 ◽  
Vol 48 (6) ◽  
pp. 1121-1137 ◽  
Author(s):  
Alberto Alzati ◽  
Marina Bertolini ◽  
Gian Mario Besana
Keyword(s):  
Elliptic Curve ◽  
Numerical Characterization ◽  
Projective Bundles ◽  
Very Ampleness

AbstractLet D be a divisor on a projectivized bundle over an elliptic curve. Numerical conditions for the very ampleness of D are proved. In some cases a complete numerical characterization is found.

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