arXiv subjects

M. E. Kazarian

Publications and source records attributed to M. E. Kazarian.

3 recordsLinked to original sources

arXiv2007

Thom polynomials for maps of curves with isolated singularities

Thom (residual) polynomials in characteristic classes are used in the analysis of geometry of functional spaces. They serve as a tool in description of classes Poincaré dual to subvarieties of functions of prescribed types. We give explicit universal expressions for residual polynomials in spaces of functions on complex curves having isolated singularities and multisingularities, in terms of few characteristic classes. These expressions lead to a partial explicit description of a stratification of Hurwitz spaces.

math.AG↗

arXiv2006

An algebro-geometric proof of Witten's conjecture

We present a new proof of Witten's conjecture. The proof is based on the analysis of the relationship between intersection indices on moduli spaces of complex curves and Hurwitz numbers enumerating ramified coverings of the 2-sphere.

math.AG↗

arXiv1996

Giambelli-type formula for subbundles of the tangent bundle

Let us consider a generic n-dimensional subbundle V of the tangent bundle TM on some given manifold M. Given V one can define different degeneracy loci S_r(CV), r=(r_1<= r_2<= r_3<=...<=r_k) on M consisting of all points x in M for which the dimension of the subspace V^j(x) in TM(x) spanned by all length <= j commutators of vector fields tangent to V at x is less than or equal to r_j. We calculate 'explicitly' the cohomology classes dual to S_r(V) using determinantal formulas due to W.Fulton and the expression for the Chern classes of the associated bundle of free Lie algebras in terms of the Chern classes of V itself.

alg-geom↗