RT Journal Article
T1 On higher dimensional extremal varieties of general type
A1 Bangere, purnaprajna
A1 Chen, Jungkai A.
A1 Gallego Rodrigo, Francisco Javier
AB Relations among fundamental invariants play an important role in algebraic geometry. It is known that an  n -dimensional variety of general type whose image of its canonical map is of maximal dimension, satisfies Vol ≥2(pg−n). In this article, we investigate the very interesting extremal situation of varieties with Vol = 2 (pg−n), which we call Horikawa varieties for they are natural higher dimensional analogues of Horikawa surfaces.We obtain a structure theorem for Horikawa varieties and explore their pluriregularity. We use this to prove optimal results on projective normality of pluricanonical linear systems. We study the fundamental groups of Horikawa varieties, showing that they are simply connected. We prove results on deformations of Horikawa varieties, whose implications on the moduli space make them the higher dimensional analogue of curves of genus 2.Even though there are infinitely many families of Horikawa varieties in any given dimension n, we show that when the image of the canonical map is singular, the geometric genus of the Horikawa varieties is bounded by n+4.
PB The Mathematical Society of Japan
YR 2023
FD 2023-07
LK https://hdl.handle.net/20.500.14352/87664
UL https://hdl.handle.net/20.500.14352/87664
LA eng
NO University of Kansas
NO National Center for Theoretical Sciences
NO Ministry of Science and Technology of Taiwan
NO Universidad Complutense de Madrid
DS Docta Complutense
RD 10 abr 2025