Zobrazeno 1 - 10
of 35
pro vyhledávání: '"Mcfaddin, Patrick"'
Trisections of closed 4-manifolds, first defined and studied by Gay and Kirby, have proved to be a useful tool in the systematic analysis of 4-manifolds via handlebodies. Subsequent work of Abrams, Gay, and Kirby established a connection with the alg
Externí odkaz:
http://arxiv.org/abs/2406.14530
Autor:
McFaddin, Patrick K., Needham, Tom
Interleaving distances are used widely in Topological Data Analysis (TDA) as a tool for comparing topological signatures of datasets. The theory of interleaving distances has been extended through various category-theoretic constructions, enabling it
Externí odkaz:
http://arxiv.org/abs/2311.11936
Publikováno v:
In Advances in Mathematics May 2024 444
A well-known conjecture of Orlov asks whether the existence of a full exceptional collection implies rationality of the underlying variety. We prove this conjecture for arithmetic toric varieties over general fields. We also investigate a slight gene
Externí odkaz:
http://arxiv.org/abs/2009.10175
Over a non-closed field, it is a common strategy to use separable algebras as invariants to distinguish algebraic and geometric objects. The most famous example is the deep connection between Severi-Brauer varieties and central simple algebras. For m
Externí odkaz:
http://arxiv.org/abs/2006.06876
Autor:
Ballard, Matthew R., Chidambaram, Nitin K., Favero, David, McFaddin, Patrick K., Vandermolen, Robert R.
Publikováno v:
J. Math. Pures Appl. (9) 147 (2021), 29-59
We develop a generalization of the $Q$-construction of the first author, Diemer, and the third author for Grassmann flips. This generalization provides a canonical idempotent kernel on the derived category of the associated global quotient stack. The
Externí odkaz:
http://arxiv.org/abs/1904.12195
We exhibit full exceptional collections of vector bundles on any smooth, Fano arithmetic toric variety whose split fan is centrally symmetric.
Comment: 27 pages, to appear in Math. Nachr
Comment: 27 pages, to appear in Math. Nachr
Externí odkaz:
http://arxiv.org/abs/1812.09392
Publikováno v:
European Journal of Mathematics 5, 640-645 (2019)
We combine the Bondal-Uehara method for producing exceptional collections on toric varieties with a result of the first author and Favero to expand the set of varieties satisfying Orlov's Conjecture on derived dimension.
Comment: 5 pages, commen
Comment: 5 pages, commen
Externí odkaz:
http://arxiv.org/abs/1709.07128
Publikováno v:
Ann. K-Th. 4 (2019) 211-242
We begin a systematic investigation of derived categories of smooth projective toric varieties defined over an arbitrary base field. We show that, in many cases, toric varieties admit full exceptional collections. Examples include all toric surfaces,
Externí odkaz:
http://arxiv.org/abs/1709.03574
Autor:
McFaddin, Patrick K.
We compute the group of $K_1$-zero-cycles on the second generalized involution variety for an algebra of degree 4 with symplectic involution. This description is given in terms of the group of multipliers of similitudes associated to the algebra with
Externí odkaz:
http://arxiv.org/abs/1703.03826