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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.

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