6,914 research outputs found
Intersection numbers with Witten's top Chern class
Witten's top Chern class is a particular cohomology class on the moduli space
of Riemann surfaces endowed with r-spin structures. It plays a key role in
Witten's conjecture relating to the intersection theory on these moduli spaces.
Our first goal is to compute the integral of Witten's class over the
so-called double ramification cycles in genus 1. We obtain a simple closed
formula for these integrals.
This allows us, using the methods of [15], to find an algorithm for computing
the intersection numbers of the Witten class with powers of the \psi-classes
(or tautological classes) over any moduli space of r-spin structures, in short,
all numbers involved in Witten's conjecture.Comment: 27 page
On generalized Sethi-Vafa-Witten formulas
We present a formula for computing proper pushforwards of classes in the Chow
ring of a projective bundle under the projection \pi:\Pbb(\Escr)\rightarrow
B, for a non-singular compact complex algebraic variety of any dimension.
Our formula readily produces generalizations of formulas derived by Sethi,Vafa,
and Witten to compute the Euler characteristic of elliptically fibered
Calabi-Yau fourfolds used for F-theory compactifications of string vacua. The
utility of such a formula is illustrated through applications, such as the
ability to compute the Chern numbers of any non-singular complete intersection
in such a projective bundle in terms of the Chern class of a line bundle on
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
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
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