Zobrazeno 1 - 10
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pro vyhledávání: '"Brazelton A"'
Autor:
Brazelton, Thomas, Raman, Sidhanth
We explore the enumerative problem of finding lines on cubic surfaces defined by symmetric polynomials. We prove that the moduli space of symmetric cubic surfaces is an arithmetic quotient of the complex hyperbolic line, and determine constraints on
Externí odkaz:
http://arxiv.org/abs/2410.09270
Autor:
Bethea, Candace, Brazelton, Thomas
Recall that a non-singular planar quartic is a canonically embedded non-hyperelliptic curve of genus three. We say such a curve is symmetric if it admits non-trivial automorphisms. The classification of (necessarily finite) groups appearing as automo
Externí odkaz:
http://arxiv.org/abs/2410.09242
Autor:
Brazelton, Thomas, Hornslien, William
In his thesis, Cazanave proved that the set of naive $\mathbb{A}^1$-homotopy classes of endomorphisms of the projective line admits a monoid structure whose group completion is genuine $\mathbb{A}^1$-homotopy classes of endomorphisms of the projectiv
Externí odkaz:
http://arxiv.org/abs/2410.02668
Autor:
Borisov, Nikita, Brazelton, Thomas, Espino, Frenly, Hagedorn, Thomas, Han, Zhaobo, Garcia, Jordy Lopez, Louwsma, Joel, Ong, Wern Juin Gabriel, Tawfeek, Andrew R.
We describe the Macaulay2 package "A1BrouwerDegrees" for computing local and global $\mathbb{A}^1$-Brouwer degrees and studying symmetric bilinear forms over the complex numbers, the real numbers, the rational numbers, and finite fields of characteri
Externí odkaz:
http://arxiv.org/abs/2312.00106
Autor:
Brazelton, Thomas
We formulate an equivariant conservation of number, which proves that a generalized Euler number of a complex equivariant vector bundle can be computed as a sum of local indices of an arbitrary section. This involves an expansion of the Pontryagin--T
Externí odkaz:
http://arxiv.org/abs/2210.08622
Autor:
Brazelton, Thomas
Given $mp$ different $p$-planes in general position in $(m+p)$-dimensional space, a classical problem is to ask how many $p$-planes intersect all of them. For example when $m = p = 2$, this is precisely the question of "lines meeting four lines in 3-
Externí odkaz:
http://arxiv.org/abs/2206.01143
Publikováno v:
In Journal of Number Theory November 2024 264:1-26
Autor:
Brazelton, Thomas, McKean, Stephen
Publikováno v:
Math. Scand. 129(1), 5--38 (2023)
One can compute the local $\mathbb{A}^1$-degree at points with separable residue field by base changing, working rationally, and post-composing with the field trace. We show that for endomorphisms of the affine line, one can compute the local $\mathb
Externí odkaz:
http://arxiv.org/abs/2112.04592
By a theorem of Johansson, every triangle-free graph $G$ of maximum degree $\Delta$ has chromatic number at most $(C+o(1))\Delta/\log \Delta$ for some universal constant $C > 0$. Using the entropy compression method, Molloy proved that one can in fac
Externí odkaz:
http://arxiv.org/abs/2109.13376
Publikováno v:
Alg. Number Th. 17 (2023) 1985-2012
We prove that both the local and global $\mathbb{A}^1$-degree of an endomorphism of affine space can be computed in terms of the multivariate B\'ezoutian. In particular, we show that the B\'ezoutian bilinear form, the Scheja--Storch form, and the $\m
Externí odkaz:
http://arxiv.org/abs/2103.16614