Geometry of the Plane Cremona Maps

By Maria Alberich-Carramiñana. 2001

128 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/0b56d191bf248b2d0be481e57d9f93d5a59a968b

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In Biomedical Engineering

In Geometry and Topology

Citations in the corpus

Lagrangian spheres, symplectic surfaces and the symplectic mapping class group (2010, background): “Noether, which asserts that a birational automorphism of CP 2 (also known as plane Cremona map) can be decomposed into a series of ordinary quadratic transformations (see [1] for a complete account).”
Plane Cremona maps: saturation and regularity of the base ideal (2011, methodology): “,μr} of multiplicities corresponding to the base points, preceded by the degree d of F , is the characteristic [1] of F – usually denoted (d;μ1, .”
Topics in classical algebraic geometry (2006, background): “Take a point(x[0], y[0]) ∈ R and let(x[1], y[1]) ∈ R be defined as follows: y[1] is the second point on S on the tangent tox[0], x[1] 6= x[0] is the point where the tangent of C at [x[1] containsy[1].”
Classical Algebraic Geometry: A Modern View (2012, background): “Since the 2-torsion subgroup Jac(C)[2] is isomorphic to (Z/2Z) , there are 2 theta characteristics.”
Dynamical degrees of birational transformations of projective surfaces (2013, background): “The result follows from NoetherCastelnuovo theorem, which asserts that Bir(P(2)k) is generated by Aut(P(2)k) and the standard quadratic transformation, when k is algebraically closed (see [28] or [1]).”
Finite Subgroups of the Plane Cremona Group (2006, background): “t acts on K with eigenvalues −1,1. Otherwise it acts identically on K. The product (12)(34) acts with eigenvalues (−1,−1,1), so if it ﬁxes nK then it acts as the minus identity on K. In our case nK = [1,2,0,0]and (12),(12)(34) ∈22 ﬁx nK. Accordingly, (12) acts as (−1,1) giving a subgroup K: 2 ∼=3×S3”