Academic literature on the topic 'Ample sets'

The present study sets out to discuss World Literature Paradigm in a Romanian context, by undertaking an ample journey through the most important present-day theories, while also adding local definitions of the concept to them. Our discussion is centred o

AbstractWe consider the surface obtained from the projective plane by blowing up the points of intersection of two plane curves meeting transversely. We find minimal generating sets of the defining ideals of these surfaces embedded in projective space by the sections of a very ample divisor class. All of the results are proven over an algebraically closed field of arbitrary characteristic.

Let $f : X \to S$ be a family of smooth projective algebraic varieties over a smooth connected quasi-projective base $S$ , and let $\mathbb {V} = R^{2k} f_{*} \mathbb {Z}(k)$ be the integral variation of Hodge structure coming from degree $2k$ cohomology it induces. Associated to $\mathbb {V}$ one has the so-called Hodge locus $\textrm {HL}(S) \subset S$ , which is a countable union of ‘special’ algebraic subvarieties of $S$ parametrizing those fibres of $\mathbb {V}$ possessing extra Hodge tensors (and so, conjecturally, those fibres of $f$ possessing extra algebraic cycles). The special subvarieties belong to a larger class of so-called weakly special subvarieties, which are subvarieties of $S$ maximal for their algebraic monodromy groups. For each positive integer $d$ , we give an algorithm to compute the set of all weakly special subvarieties $Z \subset S$ of degree at most $d$ (with the degree taken relative to a choice of projective compactification $S \subset \overline {S}$ and very ample line bundle $\mathcal {L}$ on $\overline {S}$ ). As a corollary of our algorithm we prove conjectures of Daw–Ren and Daw–Javanpeykar–Kühne on the finiteness of sets of special and weakly special subvarieties of bounded degree.

‘Statius’Thebaid’, someone donnishly quipped, ‘has no sufficient reason to exist.’ Kyle Gervais might beg to differ. Like theThebaiditself, his commentary on Book 2 has grown over many years, and deserves to be taken very seriously. The crisp introduction sets the tone and clearly signals priorities in its four sections, a rising tetracolon for author, problems of editing, intratexts, and intertexts; not a word on style and prosody, and reception is excluded on the ground that Statius’ ownimitatiois quite enough to be getting on with. The text is newly constituted, with ample apparatus and text-critical discussion: Gervais joins Barrie Hall's rebellion against the bifid stemma, but fairly questions his view that theThebaidshould be easy reading; he accordingly diverges from his edition nearly a hundred times, and offers a translation which, if less old-falutin’ than Shack's Loeb, does an equally good job of disabusing anyone who thought it would be quicker to read Statius in English. The notes are full and rich: words aren't wasted, but both philological graft and literary interpretation amply attest to fine scholarship, good sense, and long thought.