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Let X be a smooth, complex Fano variety, and delta(X) its Lefschetz defect. It is known that if delta(X) is at least 4, then X is isomorphic to a product SxT, where dim T=dim X-2. In this paper we prove a structure theorem for the case where delta(X)
Externí odkaz:
http://arxiv.org/abs/2201.02413
Autor:
Casagrande, C.
Let X be a smooth complex Fano 4-fold. We show that if X has a small elementary contraction, then the Picard number rho(X) of X is at most 12. This result is based on a careful study of the geometry of X, on which we give a lot of information. We als
Externí odkaz:
http://arxiv.org/abs/2106.09264
Building on the work of Mukai, we explore the birational geometry of the moduli spaces M_{S,L} of semistable rank two torsion-free sheaves, with c_1=-K_S and c_2=2, on a polarized degree one del Pezzo surface (S,L); this is related to the birational
Externí odkaz:
http://arxiv.org/abs/1707.09152
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Autor:
Casagrande, C.
Let N be the moduli space of stable rank 2 quasiparabolic vector bundles of fixed degree on the projective line with 2g+1 marked points, where g>1, and stability is with respect to the weights {0,1/2} at each marked point. In this note we show that N
Externí odkaz:
http://arxiv.org/abs/1410.3087
Autor:
Casagrande, C.
Let X be a smooth, complex Fano variety. For every prime divisor D in X, we set c(D):=dim ker(r:H^2(X,R)->H^2(D,R)), where r is the natural restriction map, and we define an invariant of X as c_X:=max{c(D)|D is a prime divisor in X}. In a previous pa
Externí odkaz:
http://arxiv.org/abs/1307.5418
Autor:
Casagrande, C.
Let X be a (smooth, complex) Fano 4-fold. For any prime divisor D in X, consider the image of N_1(D) in N_1(X) under the push-forward of 1-cycles, and let c_D be its codimension in N_1(X). We define an integral invariant c_X of X as the maximal c_D,
Externí odkaz:
http://arxiv.org/abs/1201.5464
Autor:
Casagrande, C.
Let X be a complex Fano manifold of arbitrary dimension, and D a prime divisor in X. We consider the image H of N_1(D) in N_1(X) under the natural push-forward of 1-cycles. We show that the codimension c of H in N_1(X) is at most 8. Moreover if c>2,
Externí odkaz:
http://arxiv.org/abs/0905.3239
Autor:
Casagrande, C.
Publikováno v:
Inventiones Mathematicae; Apr2024, Vol. 236 Issue 1, p1-16, 16p
