Details
| Original language | English |
|---|---|
| Pages (from-to) | 2615-2649 |
| Number of pages | 35 |
| Journal | Transactions of the American Mathematical Society |
| Volume | 369 |
| Issue number | 4 |
| Publication status | Published - 2017 |
Abstract
We associate to any complete spherical variety X a certain nonnegative rational number ℘(X), which we conjecture to satisfy the inequality ℘(X) ≤ dimX − rankX with equality holding if and only if X is isomorphic to a toric variety. We show that, for spherical varieties, our conjecture implies the generalized Mukai conjecture on the pseudo-index of smooth Fano varieties due to Bonavero, Casagrande, Debarre, and Druel. We also deduce from our conjecture a smoothness criterion for spherical varieties. It follows from the work of Pasquier that our conjecture holds for horospherical varieties. We are able to prove our conjecture for symmetric varieties.
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
- Mathematics(all)
- Applied Mathematics
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Transactions of the American Mathematical Society, Vol. 369, No. 4, 2017, p. 2615-2649.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - The generalized Mukai conjecture for symmetric varieties
AU - Gagliardi, Giuliano
AU - Hofscheier, Johannes
N1 - Publisher Copyright: ©2016 American Mathematical Society. Copyright: Copyright 2018 Elsevier B.V., All rights reserved.
PY - 2017
Y1 - 2017
N2 - We associate to any complete spherical variety X a certain nonnegative rational number ℘(X), which we conjecture to satisfy the inequality ℘(X) ≤ dimX − rankX with equality holding if and only if X is isomorphic to a toric variety. We show that, for spherical varieties, our conjecture implies the generalized Mukai conjecture on the pseudo-index of smooth Fano varieties due to Bonavero, Casagrande, Debarre, and Druel. We also deduce from our conjecture a smoothness criterion for spherical varieties. It follows from the work of Pasquier that our conjecture holds for horospherical varieties. We are able to prove our conjecture for symmetric varieties.
AB - We associate to any complete spherical variety X a certain nonnegative rational number ℘(X), which we conjecture to satisfy the inequality ℘(X) ≤ dimX − rankX with equality holding if and only if X is isomorphic to a toric variety. We show that, for spherical varieties, our conjecture implies the generalized Mukai conjecture on the pseudo-index of smooth Fano varieties due to Bonavero, Casagrande, Debarre, and Druel. We also deduce from our conjecture a smoothness criterion for spherical varieties. It follows from the work of Pasquier that our conjecture holds for horospherical varieties. We are able to prove our conjecture for symmetric varieties.
UR - http://www.scopus.com/inward/record.url?scp=85009460382&partnerID=8YFLogxK
U2 - 10.1090/tran/6738
DO - 10.1090/tran/6738
M3 - Article
AN - SCOPUS:85009460382
VL - 369
SP - 2615
EP - 2649
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
SN - 0002-9947
IS - 4
ER -