173 citations · 972 across the 64 of their papers we have counts for
50 papers · 1 filter
Quintic surfaces with 18 cusps
Lev Borisov, Carlos Rito
We construct quintic surfaces in the three-dimensional projective space with ordinary cusps. Our starting point is the Barth--Rams description of quintics contai…
Hanlon-Hicks-Lazarev resolution revisited
Lev Borisov, Zengrui Han
Hanlon, Hicks and Lazarev constructed resolutions of structure sheaves of toric substacks by certain line bundles on the ambient toric stacks. In this paper, we give a new and subs…
Adventures in algebraic geometry
Lev Borisov
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 exp…
Non-existence of phantoms on some non-generic blowups of the projective plane
Lev Borisov, Kimoi Kemboi
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.
Modular curves as moduli spaces of point arrangements and applications
Lev Borisov, Xavier Roulleau
For a complex elliptic curve and a point of order on it, the images of the points under the Weierstrass embedding of into are coll…
On the Geometry of a Fake Projective Plane with Automorphisms
Lev Borisov, Mattie Ji, Yanxin Li +1
A fake projective plane is a complex surface with the same Betti numbers as but not biholomorphic to it. We study the fake projective plane $\mathbb{P}_{\operatorn…