Zobrazeno 1 - 10
of 16
pro vyhledávání: '"Alan Stapledon"'
Publikováno v:
Algebraic Combinatorics. 3:1417-1430
Motivated by connections to intersection homology of toric morphisms, the motivic monodromy conjecture, and a question of Stanley, we study the structure of triangulations of simplices whose local h-polynomial vanishes. As a first step, we identify a
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::99c50056fcad6848e39a205455b02dda
https://doi.org/10.5802/alco.146
https://doi.org/10.5802/alco.146
Autor:
Alan Stapledon
Publikováno v:
Journal of Combinatorial Theory, Series A. 151:51-60
We show how to compute the Ehrhart polynomial of the free sum of two lattice polytopes containing the origin $P$ and $Q$ in terms of the enumerative combinatorics of $P$ and $Q$. This generalizes work of Beck, Jayawant, McAllister, and Braun, and fol
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5e9a37647a17f22555f64e74b223aa33
https://doi.org/10.1016/j.jcta.2017.04.004
https://doi.org/10.1016/j.jcta.2017.04.004
Autor:
Alan Stapledon
Publikováno v:
International Mathematics Research Notices. 2016:1497-1540
We introduce a powerful connection between Ehrhart theory and additive number theory, and use it to produce infinitely many new classes of inequalities between the coefficients of the $h^*$-polynomial of a lattice polytope. This greatly improves upon
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::38b7733d9a8e47290040a68a085bb327
https://doi.org/10.1093/imrn/rnv186
https://doi.org/10.1093/imrn/rnv186
Autor:
Dave Anderson, Alan Stapledon
Publikováno v:
Transformation Groups. 18:931-969
We present a new geometric interpretation of equivariant cohomology in which one replaces a smooth, complex $G$-variety $X$ by its associated arc space $J_{\infty} X$, with its induced $G$-action. This not only allows us to obtain geometric classes i
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a6e98f05b0853fecf8309144f39bcbef
https://doi.org/10.1007/s00031-013-9239-4
https://doi.org/10.1007/s00031-013-9239-4
Autor:
Alan Stapledon
Publikováno v:
Advances in Mathematics. 230(4-6):1557-1596
We prove a representation-theoretic version of Borisov–Batyrev mirror symmetry, and use it to construct infinitely many new pairs of orbifolds with mirror Hodge diamonds, with respect to the usual Hodge structure on singular complex cohomology. We
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4295539f3bcb0e10575bede43626e112
Autor:
Alan Stapledon
Publikováno v:
Advances in Mathematics. 226(4):3622-3654
Motivated by representation theory and geometry, we introduce and develop an equivariant generalization of Ehrhart theory, the study of lattice points in dilations of lattice polytopes. We prove representation-theoretic analogues of numerous classica
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a7e96ddb24203048c85f5cd1e7cd3f02
Autor:
Eric Katz, Alan Stapledon
The motivic nearby fiber is an invariant obtained from degenerating a complex variety over a disc. It specializes to the Euler characteristic of the original variety but also contains information on the variation of Hodge structure associated to the
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4bbca4b5daa94b4a05899c42944376af
http://arxiv.org/abs/1404.3000
http://arxiv.org/abs/1404.3000
Autor:
Eric Katz, Alan Stapledon
There are natural polynomial invariants of polytopes and lattice polytopes coming from enumerative combinatorics and Ehrhart theory, namely the $h$- and $h^*$-polynomials, respectively. In this paper, we study their generalization to subdivisions and
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5aa6c287f81a3019029ec5da92d82d88
Autor:
Alan Stapledon, Dave Anderson
Given a Schubert variety X_w, we exhibit a divisor \Delta, defined over the integers, such that the pair (X_w,\Delta) is log Fano in all characteristics.
Comment: 3 pages; to appear in Proc. Amer. Math. Soc
Comment: 3 pages; to appear in Proc. Amer. Math. Soc
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::476953657cd65564cca92dbc49e8a790
http://arxiv.org/abs/1203.6678
http://arxiv.org/abs/1203.6678
Autor:
Alan Stapledon
We establish a connection between the orbifold cohomology of hypertoric varieties and the Ehrhart theory of Lawrence polytopes. More specifically, we show that the dimensions of the orbifold cohomology groups of a hypertoric variety are equal to the
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a79ffeb7b274f7fa028a1bafcc3000f0