Zobrazeno 1 - 10
of 99
pro vyhledávání: '"Cartwright, Dustin"'
Autor:
Cartwright, Dustin, Varghese, Dony
Publikováno v:
European Journal of Combinatorics, Volume 118, May 2024, 103939
We investigate possible linear, algebraic, and Frobenius flock characteristic sets of matroids. In particular, we classify possible combinations of linear and algebraic characteristic sets when the algebraic characteristic set is finite or cofinite.
Externí odkaz:
http://arxiv.org/abs/2212.00095
Autor:
Cartwright, Dustin, Varghese, Dony
Publikováno v:
In European Journal of Combinatorics May 2024 118
Publikováno v:
Int. Math. Res. Not., 2022:3, 2298-2336
We develop the theory of matroids over one-dimensional algebraic groups, with special emphasis on positive characteristic. In particular, we compute the Lindstr\"om valuations and Frobenius flocks of such matroids. Building on work by Evans and Hrush
Externí odkaz:
http://arxiv.org/abs/1812.08692
Autor:
Cartwright, Dustin
Publikováno v:
J. Combin. Theory Ser. A 157 (2018) 389-401
Recently, Bollen, Draisma, and Pendavingh have introduced the Lindstr\"om valuation on the algebraic matroid of a field extension of characteristic p. Their construction passes through what they call a matroid flock and builds on some of the associat
Externí odkaz:
http://arxiv.org/abs/1704.08671
Autor:
Cartwright, Dustin
Publikováno v:
Compositio Math. 157 (2021) 1051-1078
We prove a specialization inequality relating the dimension of the complete linear series on a variety to the tropical complex of a regular semistable degeneration. Our result extends Baker's specialization inequality to arbitrary dimension.
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Externí odkaz:
http://arxiv.org/abs/1511.00650
Autor:
Cartwright, Dustin
Publikováno v:
in Nonarchimedean and Tropical Geometry, M. Baker, S. Payne (eds), Simons Symposia 2016
We study an obstruction to prescribing the dual complex of a strict semistable degeneration of an algebraic surface. In particular, we show that if $\Delta$ is a complex homeomorphic to a 2-dimensional manifold with negative Euler characteristic, the
Externí odkaz:
http://arxiv.org/abs/1506.04712
Autor:
Cartwright, Dustin
We study the combinatorial properties of 2-dimensional tropical complexes. In particular, we prove tropical analogues of the Hodge index theorem and Noether's formula. In addition, we introduce algebraic equivalence for divisors on tropical complexes
Externí odkaz:
http://arxiv.org/abs/1506.02023
Autor:
Cartwright, Dustin
Publikováno v:
Res. Math. Sci. 2:23 (2015)
Tropical geometry gives a bound on the ranks of divisors on curves in terms of the combinatorics of the dual graph of a degeneration. We show that for a family of examples, curves realizing this bound might only exist over certain characteristics or
Externí odkaz:
http://arxiv.org/abs/1502.03759
Publikováno v:
Collectanea Math. 67:1 (2016) 1-19
We construct immersions of trivalent abstract tropical curves in the Euclidean plane and embeddings of all abstract tropical curves in higher dimensional Euclidean space. Since not all curves have an embedding in the plane, we define the tropical cro
Externí odkaz:
http://arxiv.org/abs/1409.7372
Publikováno v:
Can. Math. Bull. 58 (2015) 250-262
Let C be a curve over a complete valued field with infinite residue field whose skeleton is a chain of loops with generic edge lengths. We prove that any divisor on the chain of loops that is rational over the value group lifts to a divisor of the sa
Externí odkaz:
http://arxiv.org/abs/1404.4001