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# Kangjin Han, On the Singular Loci of Higher Secants of Veronese Varieties

## December 9, 2021 @ 2:00 pm - 2:50 pm KST

(This is a part of *Algebraic Geometry Day at CCG in IBS.*)

For a projective variety *X* in * P^{N}*, the

*k*-secant variety

*σ*(

_{k}*X*) is defined to be the closure of the union of

*k*-planes in

*spanned by*

**P**^{N}*k*-points of

*X*. In this talk, we consider singular loci of higher secant varieties of the image of the

*d*-uple Veronese embedding of projective

*n*-space,

*ν*(

_{d}*). For the singular loci of*

**P**^{n}*k*-secant of

*ν*(

_{d}*), it has been known only for*

**P**^{n}*k≤*3. First, I will review some basic notions and results and then explain projective techniques with respect to an explicit calculation of the Gauss map of

*X*and computation for conormal space via a certain type of Young flattening. As investigating geometry of moving tangents along subvarieties, we determine the (non-)singularity of so-called ‘subsecant loci’ of

*k*-secant of

*ν*(

_{d}*) for arbitrary*

**P**^{n}*k*. This is a joint work with Katsuhisa Furukawa.