9,290 research outputs found
A Macaulay2 package for characteristic classes and the topological Euler characteristic of complex projective schemes
The Macaulay2 package CharacteristicClasses provides commands for the
computation of the topological Euler characteristic, the degrees of the Chern
classes and the degrees of the Segre classes of a closed subscheme of complex
projective space. The computations can be done both symbolically and
numerically, the latter using an interface to Bertini. We provide some
background of the implementation and show how to use the package with the help
of examples.Comment: 6 page
Computing torus-equivariant K-theory of singular varieties
This expository note surveys some results on equivariant K-theory of
varieties with a torus action, focusing on recent work with Sam Payne and
Richard Gonzales. It is based on my contribution to the Clifford Lectures at
Tulane University in March 2015.Comment: 16 page
The Euclidean distance degree of smooth complex projective varieties
We obtain several formulas for the Euclidean distance degree (ED degree) of
an arbitrary nonsingular variety in projective space: in terms of Chern and
Segre classes, Milnor classes, Chern-Schwartz-MacPherson classes, and an
extremely simple formula equating the Euclidean distance degree of X with the
Euler characteristic of an open subset of X
Segre Class Computation and Practical Applications
Let be closed (possibly singular) subschemes of a smooth
projective toric variety . We show how to compute the Segre class
as a class in the Chow group of . Building on this, we give effective
methods to compute intersection products in projective varieties, to determine
algebraic multiplicity without working in local rings, and to test pairwise
containment of subvarieties of . Our methods may be implemented without
using Groebner bases; in particular any algorithm to compute the number of
solutions of a zero-dimensional polynomial system may be used
A method to compute Segre classes of subschemes of projective space
We present a method to compute the degrees of the Segre classes of a
subscheme of complex projective space. The method is based on generic
residuation and intersection theory. It has been implemented using the software
system Macaulay2.Comment: 13 page
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