The Hilbert polynomial of a homogeneous complete intersection is determined by the degrees generators defining ideal. are not, in general, — but sometimes they are. When? We give some general criteria and completely answer question up to codimension 6.

Let M be the interior of a compact, orientable 3–manifold with non-empty boundary a disjoint union of tori, and T be an ideal triangulation of M . The affine algebraic set D(M ; T ), a subset of which parameterises (incomplete) hyperbolic structures obtained on M using T , is defined and compactified by adding projective classes of transversely measured singular codimension–one foliations of (M...

We study balanced Hermitian structures on almost abelian Lie algebras, i.e. algebras with a codimension-one ideal. In particular, we classify six-dimensional which carry structure. It has been conjectured in [1] that compact complex manifold admitting both metric and an SKT necessarily Kähler metric: prove this conjecture for solvmanifolds left-invariant structures. Moreover, investigate the be...

The Rees algebra of an ideal is a classical object that has been studied throughout many decades. Our interest to Rees algebras comes from the fact that they provide the algebraic realizations for certain class of rational n-folds, namely those obtained from P by blowing up at a subscheme. In this paper, we study the Rees algebras of certain codimension two perfect ideals. To be more precise, w...

Polynomial system solving arises in many application areas to model non-linear geometric properties. In such settings, polynomial systems may come with degeneration which the end-user wants exclude from solution set. The nondegenerate locus of a is set points where codimension matches number equations. Computing classically done through ideal-theoretic operations commutative algebra as saturati...

Abstract. Our main theorem shows that the regularity of non-degenerate homogeneous prime ideals is not bounded by any polynomial function of the degree; this holds over any field k. In particular, we provide counterexamples to the longstanding Regularity Conjecture, also known as the Eisenbud-Goto Conjecture (1984). We introduce a method which, starting from a homogeneous ideal I, produces a pr...