Zobrazeno 1 - 10
of 21
pro vyhledávání: '"14N05, 14N10"'
We introduce a theory of relative tangency for projective algebraic varieties. The dual variety $X_Z^\vee$ of a variety $X$ relative to a subvariety $Z$ is the set of hyperplanes tangent to $X$ at a point of $Z$. We also introduce the concept of pola
Externí odkaz:
http://arxiv.org/abs/2310.16766
Autor:
Chipalkatti, Jaydeep
Given six points $A,B,C,D,E,F$ on a nonsingular conic in the complex projective plane, Pascal's theorem says that the three intersection points $AE \cap BF, BD \cap CE, AD \cap CF$ are collinear. The line containing them is called a pascal, and we ge
Externí odkaz:
http://arxiv.org/abs/2303.10319
Kalman varieties of tensors are algebraic varieties consisting of tensors whose singular vector $k$-tuples lay on prescribed subvarieties. They were first studied by Ottaviani and Sturmfels in the context of matrices. We extend recent results of Otta
Externí odkaz:
http://arxiv.org/abs/2109.09481
Autor:
Ottaviani, Giorgio, Shahidi, Zahra
The first author with B. Sturmfels studied the variety of matrices with eigenvectors in a given linear subspace, called Kalman variety. We extend that study from matrices to symmetric tensors, proving in the tensor setting the irreducibility of the K
Externí odkaz:
http://arxiv.org/abs/2010.03843
Autor:
Asgarli, Shamil, Freidin, Brian
We study the asymptotic proportion of smooth plane curves over a finite field $\mathbb{F}_q$ which are tangent to every line defined over $\mathbb{F}_q$. This partially answers a question raised by Charles Favre. Our techniques include applications o
Externí odkaz:
http://arxiv.org/abs/2009.13421
In a series of papers, Aluffi and Faber computed the degree of the $GL_3$ orbit closure of an arbitrary plane curve. We attempt to generalize this to the equivariant setting by studying how orbits degenerate under some natural specializations, yieldi
Externí odkaz:
http://arxiv.org/abs/1903.10069
We study the ramification divisors of projections of a smooth projective variety onto a linear subspace of the same dimension. We prove that the ramification divisors vary in a maximal dimensional family for a large class of varieties. Going further,
Externí odkaz:
http://arxiv.org/abs/1901.01513
Consider the Fano scheme $F_k(Y)$ parameterizing $k$-dimensional linear subspaces contained in a complete intersection $Y \subset \mathbb{P}^m$ of multi-degree $\underline{d} = (d_1, \ldots, d_s)$. It is known that, if $t := \sum_{i=1}^s \binom{d_i +
Externí odkaz:
http://arxiv.org/abs/1812.06682
Autor:
Guo, Yang
In this paper, we use the properties of the self-polar triangle to not only show a novel method for a basic point-line enumerative problem of conics, but also present a series of closed-form solutions to the conics from all minimal configurations of
Externí odkaz:
http://arxiv.org/abs/1801.02751
Autor:
Bolognesi, Michele, Massarenti, Alex
Publikováno v:
Alg. Number Th. 15 (2021) 513-544
In this paper we study the geometry of GIT configurations of $n$ ordered points on $\mathbb{P}^1$ both from the the birational and the biregular viewpoint. In particular, we prove that any extremal ray of the Mori cone of effective curves of the quot
Externí odkaz:
http://arxiv.org/abs/1702.00068