Browsing by Author "Degtyarev, Alex"
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800 conics on a smooth quartic surface
Degtyarev, Alex (Elsevier BV * NorthHolland, 20220310)We construct an example of a smooth spatial quartic surface that contains 800 irreducible conics. © 2022 Elsevier B.V. 
Conics in sextic K3Surface in P4
Degtyarev, Alex (Cambridge University Press, 20211129)We prove that the maximal number of conics in a smooth sextic K3surface X ⊂ P4 is 285, whereas the maximal number of real conics in a real sextic is 261. In both extremal configurations, all conics are irreducible. 
Lines in supersingular quartics
Degtyarev, Alex (Nihon Sugakkai,Mathematical Society of Japan, 20211019)We show that the number of lines contained in a supersingular quartic surface is 40 or at most 32, if the characteristic of the field equals 2, and it is 112, 58, or at most 52, if the characteristic equals 3. If the quartic ... 
Lines on smooth polarized K3surfaces
Degtyarev, Alex (Springer, 2019)For each integer D⩾3D⩾3, we give a sharp bound on the number of lines contained in a smooth complex 2Dpolarized K3surface in PD+1PD+1. In the two most interesting cases of sextics in P4P4 and octics in P5P5, the bounds ... 
On plane sextics with double singular points
Degtyarev, Alex (Mathematical Sciences Publishers, 2013)We compute the fundamental groups of five maximizing sextics with double singular points only; in four cases, the groups are as expected. The approach used would apply to other sextics as well, given their equations. 
On the number of components of a complete intersection of real quadrics
Degtyarev, Alex; Itenberg, Ilia; Kharlamov, Viatchesla (Springer Basel, 2012)Our main results concern complete intersections of three real quadrics. We prove that the maximal number B0 2 (N) of connected components that a regular complete intersection of three real quadrics in ℙN may have differs ... 
Real algebraic curves with large finite number of real points
Brugalle, E.; Degtyarev, Alex; Itenberg, I.; Mangolte, F. (Springer, 2019)We address the problem of the maximal finite number of real points of a real algebraic curve (of a given degree and, sometimes, genus) in the projective plane. We improve the known upper and lower bounds and construct close ... 
Slopes and signatures of links
Degtyarev, Alex; Florens, V.; Lecuona, A.G. (Instytut Matematyczny,Polish Academy of Sciences, Institute of Mathematics, 20220314)We define the slope of a colored link in an integral homology sphere, associated to admissible characters on the link group. Away from a certain singular locus, the slope is a rational function which can be regarded as a ... 
Toward a generalized shapiro and shapiro conjecture
Degtyarev, Alex (Springer, 2012)We obtain a new, asymptotically better, bound g ≤ 1/4 d2 on the genus of a curve that may violate the generalized total reality conjecture. The bound covers all known cases except g = 0 (the original conjecture). 
Tritangents to smooth sextic curves
Degtyarev, Alex (Association des Annales de l'Institut Fourier, 20221021)We prove that a smooth plane sextic curve can have at most 72 tritangents, whereas a smooth real sextic may have at most 66 real tritangents. © 2022 Association des Annales de l'Institut Fourier. All rights reserved.