Concept
Projective variety
Related publications (244)
HYPERBOLA METHOD ON TORIC VARIETIES
We develop a very general version of the hyperbola method which extends the known method by Blomer and Brudern for products of projective spaces to complete smooth split toric varieties. We use it to count Campana points of bounded log-anticanonical height ...
Palaiseau2024Rational Points in the Noether-Lefschetz Locus of Moduli Spaces of K3 Surfaces
We give a characterization of rational points lying on the Noether-Lefschetz locus of moduli spaces of K3 surfaces by studying their lifting properties under some natural coverings of the ambient space. We then prove that the Bombieri-Lang conjecture impli ...
Oxford Univ Press2024K3 surfaces, cyclotomic polynomials and orthogonal groups
Let X be a complex projective K3 surface and let T-X be its transcendental lattice; the characteristic polynomials of isometries of T-X induced by automorphisms of X are powers of cyclotomic polynomials. Which powers of cyclotomic polynomials occur? The ai ...
Springer Int Publ Ag2024A smooth compactification of the space of genus two curves in projective space: via logarithmic geometry and Gorenstein curves
We construct a modular desingularisation of (M) over bar (2,n)(P-r, d)(main). The geometry of Gorenstein singularities of genus two leads us to consider maps from prestable admissible covers; with this enhanced logarithmic structure, it is possible to desi ...
GEOMETRY & TOPOLOGY PUBLICATIONS2023The Nonvanishing Problem for varieties with nef anticanonical bundle
We prove that if (X, A) is a threefold pair with mild singularities such that -(KX + A) is nef, then the numerical class of -(KX + A) is effective. ...
Berlin2023NORM TORI OF ETALE ALGEBRAS AND UNRAMIFIED BRAUER GROUPS
Eva Bayer Fluckiger, Ting-Yu Lee
Let k be a field, and let L be an etale k-algebra of finite rank. If a is an element of k(x), let X-a be the affine variety defined by N-L/k(x) = a. Assuming that L has at least one factor that is a cyclic field extension of k, we give a combinatorial desc ...
Jerusalem2023Arithmetic and geometric deformations of threefolds
Stefano Filipazzi, Fabio Bernasconi
We show that mixed-characteristic and equicharacteristic small deformations of 3-dimensional canonical (resp., terminal) singularities with perfect residue field of characteristic p>5 are canonical (resp., terminal). We discuss applications to arithmetic a ...
Hoboken2023Scalable angular spectrum propagation
Coherent field propagation is an essential computational tool in optics with applications ranging from computational optics and optical design to iterative field reconstructions. An improvement in the computational speed of current propagation methods is t ...
Washington2023Predicting Transformation Products during Aqueous Oxidation Processes: Current State and Outlook
Water quality and its impacts on human and ecosystem health presents tremendous global challenges. While oxidative water treatment can solve many of these problems related to hygiene and micropollutants, identifying and predicting transformation products f ...
2023Spatiotemporal Metabolic Liver Zonation and Consequences on Pathophysiology
Hepatocytes are the main workers in the hepatic factory, managing metabolism of nutrients and xenobiotics, production and recycling of proteins, and glucose and lipid homeostasis. Division of labor between hepatocytes is critical to coordinate complex comp ...
ANNUAL REVIEWS2023