On linear sections of the spinor tenfold.~I
Izvestiya. Mathematics , Tome 82 (2018) no. 4, pp. 694-751
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We discuss the geometry of transverse linear sections of the spinor
tenfold $X$, the connected component of the orthogonal Grassmannian
of 5-dimensional isotropic subspaces in a 10-dimensional vector space
endowed with a non-degenerate quadratic form. In particular, we show that
if the dimension of a linear section of $X$ is at least 5,
then its integral Chow motive is of Lefschetz type. We discuss the
classification of smooth linear sections of $X$ of small codimension.
In particular, we check that there is a unique isomorphism class of smooth
hyperplane sections and exactly two isomorphism classes of smooth sections
of codimension 2. Using this, we define a natural quadratic line complex
associated with a linear section of $X$. We also discuss the Hilbert schemes
of linear spaces and quadrics on $X$ and its linear sections.
Keywords:
spinor variety, linear sections, Chow motives, birational transformations,
classification of algebraic varieties, Hilbert schemes.
@article{IM2_2018_82_4_a2,
author = {A. G. Kuznetsov},
title = {On linear sections of the spinor {tenfold.~I}},
journal = {Izvestiya. Mathematics },
pages = {694--751},
publisher = {mathdoc},
volume = {82},
number = {4},
year = {2018},
language = {en},
url = {http://geodesic.mathdoc.fr/item/IM2_2018_82_4_a2/}
}
A. G. Kuznetsov. On linear sections of the spinor tenfold.~I. Izvestiya. Mathematics , Tome 82 (2018) no. 4, pp. 694-751. http://geodesic.mathdoc.fr/item/IM2_2018_82_4_a2/