Zobrazeno 1 - 10
of 37
pro vyhledávání: '"Nathan Ilten"'
Publikováno v:
Oberwolfach Reports. 19:861-927
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::555c93b691236251c18faa4ae13eb85e
https://doi.org/10.4171/owr/2022/17
https://doi.org/10.4171/owr/2022/17
Autor:
Tyler L. Kelly, Nathan Ilten
Publikováno v:
Mathematische Zeitschrift. 300:1529-1556
We study Fano schemes $F_k(X)$ for complete intersections $X$ in a projective toric variety $Y\subset \mathbb{P}^n$. Our strategy is to decompose $F_k(X)$ into closed subschemes based on the irreducible decomposition of $F_k(Y)$ as studied by Ilten a
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7608934a9750a0766ce7f994e6be7979
https://doi.org/10.1007/s00209-021-02809-4
https://doi.org/10.1007/s00209-021-02809-4
Autor:
Nathan Ilten, Milena Wrobel
Publikováno v:
Journal of Combinatorial Algebra. 4:141-166
We study full rank homogeneous valuations on (multi)-graded domains and ask when they have finite Khovanskii bases. We show that there is a natural reduction from multigraded to simply graded domains. As special cases, we consider projective coordina
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5ae17577aa07a88d39d1df6055c9e316
https://doi.org/10.4171/jca/41
https://doi.org/10.4171/jca/41
Autor:
Nathan Ilten, Yoav Len
Publikováno v:
Proceedings of the London Mathematical Society. 119:1234-1278
We study a tropical analogue of the projective dual variety of a hypersurface. When $X$ is a curve in $\mathbb{P}^2$ or a surface in $\mathbb{P}^3$, we provide an explicit description of $\text{Trop}(X^*)$ in terms of $\text{Trop}(X)$, as long as $\t
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f48c56fe2bad943a35da3e056a183a61
https://doi.org/10.1112/plms.12268
https://doi.org/10.1112/plms.12268
Autor:
Nathan Ilten, Yoav Len
We consider the tropicalization of tangent lines to a complete intersection curve $X$ in $\mathbb{P}^n$. Under mild hypotheses, we describe a procedure for computing the tropicalization of the image of the Gauss map of $X$ in terms of the tropicaliza
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c40bd92ed4689de9eb6f525f1addaf36
http://arxiv.org/abs/2104.15059
http://arxiv.org/abs/2104.15059
Autor:
Nathan Ilten, Klaus Altmann
Publikováno v:
Michigan Math. J. 69, iss. 2 (2020), 323-340
We prove Fujita’s freeness conjecture for Gorenstein complexity-one $T$ -varieties with rational singularities.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e656c85cca426f0818b8bb1895396a8d
https://doi.org/10.1307/mmj/1574326879
https://doi.org/10.1307/mmj/1574326879
Publikováno v:
manuscripta mathematica. 158:463-486
The correspondence between Gorenstein Fano toric varieties and reflexive polytopes has been generalized by Ilten and S\"u{\ss} to a correspondence between Gorenstein Fano complexity-one $T$-varieties and Fano divisorial polytopes. Motivated by the fi
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::86729f9e291ff0cc2edb3c770afc887a
https://doi.org/10.1007/s00229-018-1036-x
https://doi.org/10.1007/s00229-018-1036-x
Autor:
Nathan Ilten, Christopher Manon
Publikováno v:
International Mathematics Research Notices. 2019:4198-4232
Given an affine rational complexity-one $T$-variety $X$, we construct an explicit embedding of $X$ in affine space ${\mathbb{A}}^n$. We show that this embedding is well-poised, that is, every initial ideal of $I_X$ is a prime ideal, and we determine
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::230e095646326d18f9bdd3d73e3f29f3
https://doi.org/10.1093/imrn/rnx254
https://doi.org/10.1093/imrn/rnx254
Autor:
Alexandre Zotine, Nathan Ilten
Publikováno v:
SIAM Journal on Applied Algebra and Geometry. 1:152-174
Let $X_\mathcal{A}$ be the projective toric variety corresponding to a finite set of lattice points $\mathcal{A}$. We show that irreducible components of the Fano scheme $\mathbf{F}_k(X_\mathcal{A})$ parametrizing $k$-dimensional linear subspaces of
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4e0bbf9b7c6bc2f6bb91bc2b9f9409dd
https://doi.org/10.1137/16m1077039
https://doi.org/10.1137/16m1077039
Autor:
Nathan Ilten, Christian Haase
Adapting focal loci techniques used by Chiantini and Lopez, we provide lower bounds on the genera of curves contained in very general surfaces in Gorenstein toric threefolds. We illustrate the utility of these bounds by obtaining results on algebraic
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4b4dda062605941e5c68ba1b6be5f204
http://arxiv.org/abs/1903.02681
http://arxiv.org/abs/1903.02681