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Moduli Spaces of K3 Surfaces with Large Picard Number
Morrison has constructed a geometric relationship between K3 surfaces with large Picard number and abelian surfaces. In particular, this establishes that the period spaces of certain families of lattice polarized K3 surfaces ...
Smooth Complete Intersections with Positive-Definite Intersection Form
We classify the smooth complete intersections with positive-definite intersection form on their middle cohomology. There are two families. The first family are quadric hypersurfaces in P(4k+1) with k a positive integer. ...
Constructing pairing-friendly algebraic curves of genus 2 curves with small rho-value
For pairing-based cryptographic protocols to be both efficient and secure, the underlying genus 2 curves defined over finite fields used must satisfy pairing-friendly conditions, and have small rho-value, which are not ...