Counting Ramified Coverings and Intersection Theory on Spaces of Rational Functions I (Cohomology of Hurwitz Spaces)

2007 ◽  
Vol 7 (1) ◽  
pp. 85-107 ◽  
Author(s):  
S. Lando ◽  
D. Zvonkine
Keyword(s):  
Rational Functions ◽  
Intersection Theory ◽  
Hurwitz Spaces ◽  
Ramified Coverings

Note on the Grothendieck Group of Subspaces of Rational Functions and Shokurov's Cartier b-divisors

2014 ◽  
Vol 57 (3) ◽  
pp. 562-572
Author(s):  
Kiumars Kaveh ◽  
A. G. Khovanskii
Keyword(s):  
Algebraic Variety ◽  
Short Note ◽  
Grothendieck Group ◽  
Rational Functions ◽  
Intersection Theory ◽  
Point Of View ◽  
Intersection Numbers ◽  
Ground Field

Abstract.In a previous paper the authors developed an intersection theory for subspaces of rational functions on an algebraic variety X over k = ℂ. In this short note, we first extend this intersection theory to an arbitrary algebraically closed ground field k. Secondly we give an isomorphism between the group of Cartier b-divisors on the birational class of X and the Grothendieck group of the semigroup of subspaces of rational functions on X. The constructed isomorphism moreover preserves the intersection numbers. This provides an alternative point of view on Cartier b-divisors and their intersection theory.

scholarly journals Towards an intersection theory on Hurwitz spaces

2004 ◽  
Vol 68 (5) ◽  
pp. 935-964 ◽  
Author(s):  
M E Kazaryan ◽  
S K Lando
Keyword(s):  
Intersection Theory ◽  
Hurwitz Spaces

Application of the exp(-φ)-expansion method to the Pochhammer-Chree equation

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3347-3354 ◽  
Author(s):  
Nematollah Kadkhoda ◽  
Michal Feckan ◽  
Yasser Khalili
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Present Article ◽  
Analytical Solutions ◽  
Nonlinear Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Rational Functions ◽  
Expansion Method ◽  
Exponential Functions

In the present article, a direct approach, namely exp(-?)-expansion method, is used for obtaining analytical solutions of the Pochhammer-Chree equations which have a many of models. These solutions are expressed in exponential functions expressed by hyperbolic, trigonometric and rational functions with some parameters. Recently, many methods were attempted to find exact solutions of nonlinear partial differential equations, but it seems that the exp(-?)-expansion method appears to be efficient for finding exact solutions of many nonlinear differential equations.

scholarly journals Homotopical intersection theory I

2007 ◽  
Vol 11 (2) ◽  
pp. 939-977 ◽  
Author(s):  
John R Klein ◽  
E Bruce Williams
Keyword(s):  
Intersection Theory
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