Toric surfaces, vanishing Euler characteristic and Euler obstruction of a function

Seifert Surfaces of Maximal Euler Characteristic

Given a link L ⊂ S 3 , a Seifert surface S for L is a compact, orientable surface with boundary L. The Euler characteristic χ(L) of the link L is dened to be the maximum over all Euler characteristics χ(S) of Seifert surfaces S for L. Seifert surfaces exist for all L, and this denition presents itself with the problem of calculating χ(L). An easily applicable method for producing Seifert surfac...

The Equivariant Euler Characteristic of Real Coxeter Toric Varieties

Let W be a crystallographic Weyl group, and let TW be the complex toric variety attached to the fan of cones corresponding to the reflecting hyperplanes of W , and its weight lattice. The real locus TW (R) is a smooth, connected, compact manifold with a W -action. We give a formula for the Euler characteristic of TW (R) as a generalised character of W . In type An−1 for n odd, one obtains a gen...

Exponentiation and Euler Characteristic

Euler Characteristic of Primitive T -hypersurfaces and Maximal Surfaces

Viro method plays an important role in the study of topology of real algebraic hypersurfaces. The T -primitive hypersurfaces we study here appear as the result of Viro’s combinatorial patchworking when one starts with a primitive triangulation. We show that the Euler characteristic of the real part of such a hypersurface of even dimension is equal to the signature of its complex part. We use th...

Structure of Rational Open Surfaces with Non{positive Euler Characteristic

We study mainly connected conngurations of irreducible curves r i=1 C i on a nonsingular rational projective complex surface X such that the Euler characteristic (X n r i=1 C i) 0, hereby continuing a former conjecture of the author and work of Gurjar and Parameswaran. Roughly we show that any such connguration can be extended to another connguration s i=1 C i (r s) with still (X n s i=1 C i) 0...