Geometry of the Severi Variety

Linear Sections of the Severi Variety and Moduli of Curves

We study the Severi variety Vd,g of plane curves of degree d and geometric genus g. Corresponding to every such variety, there is a one-parameter family of genus g stable curves whose numerical invariants we compute. Building on the work of Caporaso and Harris, we derive a recursive formula for the degrees of the Hodge bundle on the families in question. For d large enough, these families induc...

Witt Groups of Hermitian Forms over a Brauer Severi Variety

Let X be a Brauer Severi variety over a field k of characteristic not 2 and let D be a division algebra over k with a k-linear involution. We investigate Witt groups of certain hermitian forms over D ⊗k OX .

The Brauer-severi Variety Associated with a Central Simple Algebra: a Survey

THE BRAUER-SEVERI VARIETY ASSOCIATED WITH A CENTRAL SIMPLE ALGEBRA: A SURVEY by

— The article describes the one-to-one correspondence between central simple algebras and Brauer-Severi varieties over a field. Non-abelian group cohomology is recalled and Galois descent is worked out in detail. The classifications of central simple algebras as well as of Brauer-Severi varieties by one and the same Galois cohomology set are explained. A whole section is devoted to the discussi...

Codimension 2 Cycles on Quadratic Weil Transfer of Biquaternionic Severi-brauer Variety

Let F be a field, B a biquaternion F -algebra, L/F an étale quadratic extension, X the Weil transfer with respect to L/F of the Severi-Brauer variety of BL. We show that the Chow group of codimension 2 cycle classes on X is torsion-free. Our Chow groups are those with integral coefficients. The motives used in the proof are the Grothendieck Chow motives (still with the integral coefficients) as...