arXiv subjects

Paul Apisa

Publications and source records attributed to Paul Apisa.

21 records · Page 2Linked to original sources

arXiv2017

Periodic Points in Genus Two: Holomorphic Sections over Hilbert Modular Varieties, Teichmuller Dynamics, and Billiards

We show that all GL(2, R)-equivariant point markings over orbit closures of primitive genus two translation surfaces arise from marking pairs of points exchanged by the hyperelliptic involution, Weierstrass points, or the golden points in the golden eigenform locus. As corollaries, we classify the holomorphically varying families of points over orbifold covers of genus two Hilbert modular surfaces, solve the finite blocking problem on genus two translation surfaces, and show that there is at most one nonarithmetic rank two orbit closure in the minimal stratum in genus four.

math.DS↗

arXiv2017

Rank One Orbit Closures in H^{hyp}(g-1,g-1)

Every GL(2,R)-orbit in hyperelliptic components of strata of abelian differentials in genus greater than two is either closed, dense, or contained in a locus of branched covers.

math.DS↗

arXiv2012

Groups with a base property analogous to that of vector spaces

A B-group is a group such that all its minimal generating sets (with respect to inclusion) have the same size. We prove that the class of finite B-groups is closed under taking quotients and that every finite B-group is solvable. Via a complete classification of Frattini-free finite B-groups we obtain a general structure theorem for finite B-groups. Applications include new proofs for the characterization of finite matroid groups and the classification of finite groups with the basis property.

math.GR↗