11 research outputs found
An effective method to compute closure ordering for nilpotent orbits of -representations
We develop an algorithm for computing the closure of a given nilpotent
-orbit in \g_1, where \g_1 and are coming from a or a
-grading \g= \bigoplus \g_i of a simple complex Lie algebra \g
Linear groups and computation
Funding: A. S. Detinko is supported by a Marie Skłodowska-Curie Individual Fellowship grant (Horizon 2020, EU Framework Programme for Research and Innovation).We present an exposition of our ongoing project in a new area of applicable mathematics: practical computation with finitely generated linear groups over infinite fields. Methodology and algorithms available for practical computation in this class of groups are surveyed. We illustrate the solution of hard mathematical problems by computer experimentation. Possible avenues for further progress are discussed.PostprintPeer reviewe
Linear groups and computation
We present an exposition of our ongoing project in a new area of applicable mathematics: practical computation with finitely generated linear groups over infinite fields. Methodology and algorithms available for this class of groups are surveyed. We illustrate the solution of hard mathematical problems by computer experimentation. Possible avenues for further progress are discussed
Sets of Special Subvarieties of Bounded Degree
Let be a family of smooth projective algebraic varieties over a
smooth connected quasi-projective base , and let be the integral variation of Hodge structure coming from degree
cohomology it induces. Associated to one has the so-called
Hodge locus , which is a countable union of "special"
algebraic subvarieties of parametrizing those fibres of
possessing extra Hodge tensors (and so conjecturally, those fibres of
possessing extra algebraic cycles). The special subvarieties belong to a larger
class of so-called weakly special subvarieties, which are subvarieties of
maximal for their algebraic monodromy groups. For each positive integer , we
give an algorithm to compute the set of all weakly special subvarieties of degree at most (with the degree taken relative to a choice of
projective compactification and very ample line bundle
on ). As a corollary of our algorithm we prove
conjectures of Daw-Ren and Daw-Javanpeykar-K\"uhne on the finiteness of sets of
special and weakly special subvarieties of bounded degree