arXiv subjects

Stefan Tohaneanu

Publications and source records attributed to Stefan Tohaneanu.

20 records · Page 2Linked to original sources

arXiv2014

The ubiquity of Sylvester forms in almost complete intersections

The subject matter is the structure of the Rees algebra of almost complete intersection ideals of finite colength in low-dimensional polynomial rings over fields. The main tool is a mix of Sylvester forms and iterative mapping cone construction. The material developed spins around ideals of forms in two or three variables in the search of those classes for which the corresponding Rees ideal is generated by Sylvester forms and is almost Cohen--Macaulay. A main offshoot is in the case where the forms are monomials. Another consequence is a proof that the Rees ideals of the base ideals of certain plane Cremona maps (e.g., de Jonquières maps) are generated by Sylvester forms and are almost Cohen--Macaulay.

math.AC↗

arXiv2012

Modular decomposition of the Orlik-Terao algebra of a hyperplane arrangement

Let A be a collection of n linear hyperplanes in k^l, where k is an algebraically closed field. The Orlik-Terao algebra of A is the subalgebra R(A) of the rational functions generated by reciprocals of linear forms vanishing on hyperplanes of A. It determines an irreducible subvariety of projective space. We show that a flat X of A is modular if and only if R(A) is a split extension of the Orlik-Terao algebra of the subarrangement A_X. This provides another refinement of Stanley's modular factorization theorem and a new characterization of modularity, similar in spirit to the modular fibration theorem of Paris. We deduce that if A is supersolvable, then its Orlik-Terao algebra is Koszul. In certain cases, the algebra is also a complete intersection, and we characterize when this happens.

math.AC↗