

Iskovskikh Seminar
March 19, 2015 18:00, Moscow, Steklov Mathematical Institute, room 540






The extension of varieties defined by quadratic equations
E. A. Yasinsky^{} ^{} Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

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Abstract:
We say that a smooth projective variety $V\subset\mathbb{P}^n$ extends $m$
steps nontrivially if there exists a projective variety
$W\subset\mathbb{P}^{n+m}$ such that $V=W\cap\mathbb{P}^n$, where $W$ is not
a cone, is nonsingular along $V$, and is transversal to $\mathbb{P}^n$.
Following S. Lvovski's work, we describe some classes of varieties which
have nontrivial extension and give some estimates for the number of steps
$m$ as well.

