Four Counterexamples in Combinatorial Algebraic Geometry

87 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Regularity jumps for powers of ideals (2003, background): “haracteristic 0. But the ﬁrst syzygies of a monomial ideals are independent of charK. So we may conclude that reg(I) = 3 and reg(I2) > 6 for every base ﬁeld K. The third example is dueto Sturmfels [S]. It is monomial, square-free and characteristic free. It is deﬁned by 8 square-free monomials an”
Monomial ideals whose powers have a linear resolution (2003, unknown): “Ifthebase eld hascharacteristic 2,then I itselfhasno linearresolution.”
Powers of Ideals and Fibers of Morphisms (2008, background): “ty of the ﬁbers of φ over y ∈ Y , where φ−1(y) is considered as a subscheme of Pn. From an algebraic point of view, our formula is related to the theorem of Cutkosky-Herzog-Trung [1999] and Kodiyalam [2000] showing that for any homogeneous ideal I in a standard graded algebra S, regIt can be written”
Castelnuovo-Mumford regularity of products of ideals (2002, background): “One may wonder whether the same relation holds also for the Castelnuovo-Mumford regularity, that is, whether reg(IM) ≤ reg(M) + reg(I).”