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Title: Geometric invariants and Geometric consistency of Manin’s conjecture
Authors: Sengupta, Akash Kumar
Advisors: Kollár, János
Contributors: Mathematics Department
Keywords: Algebraic Geometry
Manin's conjecture
Minimal Model Program
Number Theory
Rational points
Subjects: Mathematics
Issue Date: 2019
Publisher: Princeton, NJ : Princeton University
Abstract: Manin’s conjeture states that the asymptotic growth of the number of rational points on a Fano variety over a number field is governed by certain geometric invariants (a and b-constants). In this thesis we study the behaviour of these geometric invariants and show that Manin’s conjecture is geometrically consistent. In the first part, we study the behaviour of the b-constant in families and show that the b-constant is constant on very general fibers of a family of algebraic varieties. If the fibers of the family are uniruled, then we show that the b-constant is constant on general fibers. In the second part, we study the behaviour of the a-constant (Fujita invariant) under pull-back to generically finite covers and prove a conjecture of Lehmann-Tanimoto about finiteness of covers. In the last part, based on joint work with B. Lehmann and S. Tanimoto, we prove geometric consistency of Manin’s conjecture by showing that the rational points contributed by subvarieties or covers with larger geometric invariants are contained in a thin set.
Alternate format: The Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog:
Type of Material: Academic dissertations (Ph.D.)
Language: en
Appears in Collections:Mathematics

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