Holomorphic maps between projective spaces are maximally singular
Event details
| Date | 16.02.2016 |
| Hour | 15:15 › 17:00 |
| Speaker | László M. Fehér (ELTE Budapest) |
| Location | |
| Category | Conferences - Seminars |
The topic of the talk is the principle (singularity principle for short) expressed in the title. This is joint work with András Némethi.
In the first part of the talk I explain the following variant:
Theorem: Let $f:P^n\to P^{n+l}$ be a non-linear holomorphic map between projective spaces. Then for any s such that s(s+l)<n+1 there is a point in $P^n$, where the kernel of the differential $df_x$ is at least s dimensional.
Notice that s(s+l) is the expected codimension of the degeneracy locus of such points.
To follow the first part only some familiarity with the notion of Chern classes is necessary.
In the second part of the talk I talk about a generalization where we show that the degeneracy locus of any contact singularity (with the condition that its expected dimension is non-negative) is not empty. We can prove this generalization in "almost all" cases, and conjecture that it always holds. The proof relies on basic properties of equivariant cohomology and Thom polynomials.
Some variants of the singularity principle are valid for smooth maps between real projective spaces.
In the first part of the talk I explain the following variant:
Theorem: Let $f:P^n\to P^{n+l}$ be a non-linear holomorphic map between projective spaces. Then for any s such that s(s+l)<n+1 there is a point in $P^n$, where the kernel of the differential $df_x$ is at least s dimensional.
Notice that s(s+l) is the expected codimension of the degeneracy locus of such points.
To follow the first part only some familiarity with the notion of Chern classes is necessary.
In the second part of the talk I talk about a generalization where we show that the degeneracy locus of any contact singularity (with the condition that its expected dimension is non-negative) is not empty. We can prove this generalization in "almost all" cases, and conjecture that it always holds. The proof relies on basic properties of equivariant cohomology and Thom polynomials.
Some variants of the singularity principle are valid for smooth maps between real projective spaces.
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