Bounds on the Torsion Subgroups of Néron–Severi Groups

Let 𝑋 ⤷ Pʳ be a smooth projective variety defined by homogeneous polynomials of degree ≤ 𝑑 over an algebraically closed field 𝑘. Let Pic 𝑋 be the Picard scheme of 𝑋, and let Pic⁰ 𝑋 be the identity component of Pic 𝑋. The Néron–Severi group scheme of 𝑋 is defined by NS 𝑋 = (Pic 𝑋)/(Pic⁰ 𝑋)ᵣₑ subscript d, and the Néron–Severi group of 𝑋 is defined by NS 𝑋 = (NS 𝑋)(𝑘). We give an explicit upper bound on the order of the finite group (NS 𝑋)ₜₒᵣ and the finite group scheme (NS 𝑋)ₜₒᵣ in terms of 𝑑 and 𝑟. As a corollary, we give an upper bound on the order of the torsion subgroup of second cohomology groups of 𝑋 and the finite group [mathematical equation]. We also show that (NS 𝑋)ₜₒᵣ is generated by (deg 𝑋 − 1)(deg 𝑋 − 2) elements in various situations.

Name thesis:degree_name

Doctoral

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Mathematics

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2021

Author dc:creator

• Kweon, Hyuk Jun

Advisor dc:contributor.advisor

• Poonen, Bjorn

Statement dc:rights

• In Copyright - Educational Use Permitted
• Copyright MIT

Licence dc:rights.uri

• http://rightsstatements.org/page/InC-EDU/1.0/

Handle dc:identifier.uri

https://hdl.handle.net/1721.1/139463

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/139463