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pro vyhledávání: '"Borisov, Lev A."'
Autor:
Borisov, Lev
These notes are loosely based on an introductory course in algebraic geometry given at Rutgers University in Spring of 2024. We introduce some relatively advanced topics at the expense of the technical details.
Comment: 143 pages
Comment: 143 pages
Externí odkaz:
http://arxiv.org/abs/2407.10041
Autor:
Borisov, Lev, Kemboi, Kimoi
We show that blowups of the projective plane at points lying on a smooth cubic curve do not contain phantoms, provided the points are chosen in very general position on this curve.
Comment: 5 pages
Comment: 5 pages
Externí odkaz:
http://arxiv.org/abs/2405.01683
Autor:
Borisov, Lev, Roulleau, Xavier
For a complex elliptic curve $E$ and a point $p$ of order $n$ on it, the images of the points $p_k=kp$ under the Weierstrass embedding of $E$ into $\mathbb{C}\mathbb{P}^2$ are collinear if and only if the sum of indices is divisible by $n$. Thus, it
Externí odkaz:
http://arxiv.org/abs/2404.04364
Autor:
Borisov, Lev, Duncan, Alexander
A line bundle is immaculate if its cohomology vanishes in every dimension. We give a criterion for when a smooth toric Deligne-Mumford stack has infinitely many immaculate line bundles. This answers positively a question of Borisov and Wang. As a byp
Externí odkaz:
http://arxiv.org/abs/2312.02885
We find explicit equations of the fake projective plane $(a=7,p=2,\emptyset,D_3 X_7)$, which lies in the same class as the fake projective plane $(a=7,p=2,\emptyset,D_3 2_7)$ with $21$ automorphisms whose equations were previously found by Borisov an
Externí odkaz:
http://arxiv.org/abs/2308.14237
A fake projective plane is a complex surface with the same Betti numbers as $\mathbb{C} P^2$ but not biholomorphic to it. We study the fake projective plane $\mathbb{P}_{\operatorname{fake}}^2 = (a = 7, p = 2, \emptyset, D_3 2_7)$ in the Cartwright-S
Externí odkaz:
http://arxiv.org/abs/2308.10429
Autor:
Borisov, Lev, Lihn, Zachary
Fake projective planes are smooth complex surfaces of general type with Betti numbers equal to that of the usual projective plane. Recent explicit constructions of fake projective planes embed them via their bicanonical embedding in $\mathbb P^9$. In
Externí odkaz:
http://arxiv.org/abs/2301.09155
Autor:
Borisov, Lev, Han, Zengrui
Publikováno v:
Advances in Mathematics, Volume 442 (2024), 109582
We give an explicit formula for the duality, previously conjectured by Horja and Borisov, of two systems of GKZ hypergeometric PDEs. We prove that in the appropriate limit this duality can be identified with the inverse of the Euler characteristics p
Externí odkaz:
http://arxiv.org/abs/2301.01374
Autor:
Borisov, Lev
Publikováno v:
Ãpijournal de Géométrie Algébrique, Volume 7 (May 30, 2023) epiga:8507
We study Dolgachev elliptic surfaces with a double and a triple fiber and find explicit equations of two new pairs of fake projective plane with $21$ automorphisms, thus finishing the task of finding explicit equations of fake projective planes with
Externí odkaz:
http://arxiv.org/abs/2109.02070
Let $V$ be a $6$-dimensional complex vector space with an involution $\sigma$ of trace $0$, and let $W \subseteq \operatorname{Sym}^2 V^\vee$ be a generic $3$-dimensional subspace of $\sigma$-invariant quadratic forms. To these data we can associate
Externí odkaz:
http://arxiv.org/abs/2108.07768