scholarly journals Construction of Brauer-Severi Varieties

2021 ◽  
pp. 279-292
Author(s):  
Elisa Lorenzo García
Keyword(s):  
Severi Varieties

In this paper, we give an algorithm for computing equations of Brauer-Severi varieties over fields of characteristic 0. As an example, we show the equations of all Brauer-Severi surfaces defined over Q.

scholarly journals On universal Severi varieties of low genus K3 surfaces

2011 ◽  
Vol 271 (3-4) ◽  
pp. 953-960 ◽  
Author(s):  
Ciro Ciliberto ◽  
Thomas Dedieu
Keyword(s):  
K3 Surfaces ◽  
Severi Varieties

SEVERI VARIETIES

1986 ◽  
Vol 54 (1) ◽  
pp. 113-127 ◽  
Author(s):  
F L Zak
Keyword(s):  
Severi Varieties

scholarly journals The irreducibility of the generalized Severi varieties

2019 ◽  
Vol 119 (6) ◽  
pp. 1431-1463
Author(s):  
Adrian Zahariuc
Keyword(s):  
Severi Varieties

scholarly journals Some remarks on the Severi varieties of surfaces inℙ3

2001 ◽  
Vol 26 (1) ◽  
pp. 1-5 ◽  
Author(s):  
Xi Chen
Keyword(s):  
Severi Varieties ◽  
Curves On Surfaces

Continuing the work of Chiantini and Ciliberto (1999) on the Severi varieties of curves on surfaces inℙ3, we complete the proof of the existence of regular components for such varieties.

scholarly journals Constructions of Brauer-Severi Varieties and Norm Hypersurfaces

1990 ◽  
Vol 42 (2) ◽  
pp. 230-238 ◽  
Author(s):  
Ming-Chang Kang
Keyword(s):  
Function Field ◽  
Splitting Field ◽  
Severi Varieties ◽  
Severi Variety ◽  
Central Simple

Let k be any field, A a central simple k-algebra of degree m (i.e., dimk A = m2). Several methods of constructing the generic splitting fields for A are proposed and Saltman proves that these methods result in almost the same generic splitting field [8, Theorems 4.2 and 4.4]. In fact, the generic splitting field constructed by Roquette [7] is the function field of the Brauer- Severi variety Vm(A) while the generic splitting field constructed by Heuser and Saltman [4 and 8] is the function field of the norm surface W(A). In this paper, to avoid possible confusion about the dimension, we shall call it the norm hypersurface instead of the norm surface.

Hyperelliptic d-Tangential Covers and d× d-Matrix KdV Elliptic Solitons

2018 ◽  
Vol 2020 (23) ◽  
pp. 9539-9558
Author(s):  
Armando Treibich
Keyword(s):  
Riemann Surface ◽  
Compact Riemann Surface ◽  
Kdv Equation ◽  
Rational Surface ◽  
Geometric Condition ◽  
Kp Equation ◽  
Nodal Curves ◽  
Severi Varieties ◽  
The Kdv Equation ◽  
Elliptic Solitons

Abstract More than $40$ years ago I. Krichever developed the Theory of (vector) Baker–Akhiezer functions and devised a criterion for a $d$-marked compact Riemann surface to provide $d\times d$-matrix solutions to the KdV equation. Later on he also found a criterion for a $d$-marked curve to provide $d\times d$-matrix solutions to the Kadomtsev-Petviashvili (KP) equation, doubly periodic with respect to $x$, the 1st KP flow. In particular, when both criteria apply, one should obtain $d\times d$-matrix KdV elliptic solitons. It seems, however, that the latter issue has been completely neglected until very recently (cf. [10] where the $d=2$ case is treated). In this article we fix a complex elliptic curve $X=\mathbb{C}/\Lambda$, corresponding to a lattice $\Lambda \subset \mathbb{C}$, and define so-called hyperelliptic $d$-tangential covers as $d$-marked covers of $X$ satisfying a geometric condition inside their Jacobians. They satisfy Krichever’s criteria and give rise, therefore, to families of $d\times d$-matrix KdV elliptic solitons. We also construct an anticanonical rational surface ${\mathcal S}$ naturally attached to $X$, with a Picard group of rank $10$. It turns out that the former covers of $X$ correspond to rational irreducible curves in suitable divisor classes of ${\mathcal S}$. We thus reduce their construction to proving that the associated Severi Varieties (of rational irreducible nodal curves) are not empty. The final key to the problem consists in finding rational reducible nodal curves in the latter divisor classes that can be deformed to irreducible ones, according to A. Tannenbaum’s criterion (see [5]). At last we deduce, for any $d\geq 2$, infinite families (of arbitrary high genus and degree) of hyperelliptic $d$-tangential covers, giving rise to $d\times d$-matrix KdV elliptic solitons.

scholarly journals Severi varieties and their varieties of reductions

2005 ◽  
Vol 2005 (585) ◽  
pp. 93-139 ◽  
Author(s):  
A. Iliev ◽  
L. Manivel
Keyword(s):  
Severi Varieties
Sign in / Sign up

Export Citation Format

Share Document