Singularity Theory and Algebraic Geometry
http://hdl.handle.net/20.500.11824/18
2019-07-12T04:35:36ZA Lê-Greuel type formula for the image Milnor number
http://hdl.handle.net/20.500.11824/992
A Lê-Greuel type formula for the image Milnor number
Nuño-Ballesteros J.J.; Pallarés Torres I.
Let $f\colon (\mathbb{C}^n,0)\to (\mathbb{C}^{n+1},0)$ be a corank 1 finitely determined map germ. For a generic linear form $p\colon (\mathbb{C}^{n+1},0)\to(\mathbb{C},0)$ we denote by $g\colon (\mathbb{C}^{n-1},0)\to (\mathbb{C}^{n},0)$ the transverse slice of $f$ with respect to $p$. We prove that the sum of the image Milnor numbers $\mu_I(f)+\mu_I(g)$ is equal to the number of critical points of $p|_{X_s}\colon X_s\to\mathbb{C}$ on all the strata of $X_s$, where $X_s$ is the disentanglement of $f$ (i.e., the image of a stabilisation $f_s$ of $f$).
2019-02-01T00:00:00ZExamples of varieties with index one on C1 fields
http://hdl.handle.net/20.500.11824/990
Examples of varieties with index one on C1 fields
Dan A.; Kaur I.
Let K be the fraction field of a Henselian discrete valuation ring with algebraically closed residue field k. In this article we give a sufficient criterion for a projective variety over such a field to have index 1.
2019-04-16T00:00:00ZPerverse sheaves on semi-abelian varieties -- a survey of properties and applications
http://hdl.handle.net/20.500.11824/977
Perverse sheaves on semi-abelian varieties -- a survey of properties and applications
Liu Y.; Maxim L.; Wang B.
We survey recent developments in the study of perverse sheaves on semi-abelian varieties. As concrete applications, we discuss various restrictions on the homotopy type of complex algebraic manifolds (expressed in terms of their cohomology jump loci), homological duality properties of complex algebraic manifolds, as well as new topological characterizations of semi-abelian varieties.
2019-05-01T00:00:00ZOn Lipschitz rigidity of complex analytic sets
http://hdl.handle.net/20.500.11824/970
On Lipschitz rigidity of complex analytic sets
Fernandes A.; Sampaio J. E.
We prove that any complex analytic set in $\mathbb{C}^n$ which is Lipschitz normally embedded at infinity and has tangent cone at infinity that is a linear subspace of $\mathbb{C}^n$ must be an affine linear subspace of $\mathbb{C}^n$ itself. No restrictions on the singular set, dimension nor codimension are required. In particular, any complex algebraic set in $\mathbb{C}^n$ which is Lipschitz regular at infinity is an affine linear subspace.
2019-02-26T00:00:00Z