TY - JOUR
T1 - Linear subspaces of minimal codimension in hypersurfaces
AU - Kazhdan, David
AU - Polishchuk, Alexander
N1 - Publisher Copyright:
© 2023 International Press of Boston, Inc.. All rights reserved.
PY - 2023
Y1 - 2023
N2 - Let k be a perfect field and let X ⊂ PN be a hypersurface of degree d defined over k and containing a linear subspace L defined over k with codimPNL = r. We show that X contains a linear subspace L0 defined over k with codimPNL ≤ dr. We conjecture that the intersection of all linear subspaces (over k) of minimal codimension r contained in X, has codimension bounded above only in terms of r and d. We prove this when either d ≤ 3 or r ≤ 2.
AB - Let k be a perfect field and let X ⊂ PN be a hypersurface of degree d defined over k and containing a linear subspace L defined over k with codimPNL = r. We show that X contains a linear subspace L0 defined over k with codimPNL ≤ dr. We conjecture that the intersection of all linear subspaces (over k) of minimal codimension r contained in X, has codimension bounded above only in terms of r and d. We prove this when either d ≤ 3 or r ≤ 2.
UR - http://www.scopus.com/inward/record.url?scp=85164524923&partnerID=8YFLogxK
U2 - 10.4310/mrl.2023.v30.n1.a7
DO - 10.4310/mrl.2023.v30.n1.a7
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AN - SCOPUS:85164524923
SN - 1073-2780
VL - 30
SP - 143
EP - 166
JO - Mathematical Research Letters
JF - Mathematical Research Letters
IS - 1
ER -