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Chen–Ruan Cohomology of ℳ 1 , n and ℳ ¯ 1 , n

Nicola Pagani (2013)

Annales de l’institut Fourier

In this work we compute the Chen–Ruan cohomology of the moduli spaces of smooth and stable n -pointed curves of genus 1 . In the first part of the paper we study and describe stack theoretically the twisted sectors of ℳ 1 , n and ℳ ¯ 1 , n . In the second part, we study the orbifold intersection theory of ℳ ¯ 1 , n . We suggest a definition for an orbifold tautological ring in genus 1 , which is a subring of both the Chen–Ruan cohomology and of the stringy Chow ring.

Chern classes of reductive groups and an adjunction formula

Valentina Kiritchenko (2006)

Annales de l’institut Fourier

In this paper, I construct noncompact analogs of the Chern classes for equivariant vector bundles over complex reductive groups. For the tangent bundle, these Chern classes yield an adjunction formula for the (topological) Euler characteristic of complete intersections in reductive groups. In the case where a complete intersection is a curve, this formula gives an explicit answer for the Euler characteristic and the genus of the curve. I also prove that the higher Chern classes vanish. The first...

Chern numbers of a Kupka component

Omegar Calvo-Andrade, Marcio G. Soares (1994)

Annales de l'institut Fourier

We will consider codimension one holomorphic foliations represented by sections ω ∈ H 0 ( ℙ n , Ω 1 ( k ) ) , and having a compact Kupka component K . We show that the Chern classes of the tangent bundle of K behave like Chern classes of a complete intersection 0 and, as a corollary we prove that K is a complete intersection in some cases.

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