# Professor Paolo Cascini

Faculty of Natural SciencesDepartment of Mathematics

Professor of Mathematics

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### Contact

+44 (0)20 7594 8861p.cascini

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### Location

676Huxley BuildingSouth Kensington Campus

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## Publications

Publication Type
Year
to

30 results found

Cascini P, Floris E, 2018, On invariance of plurigenera for foliations on surfaces, JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, Vol: 744, Pages: 201-236, ISSN: 0075-4102

JOURNAL ARTICLE

Cascini P, Tanaka H, Purely log terminal threefolds with non-normal centres in characteristic two, American Journal of Mathematics, ISSN: 0002-9327

We show that many classical results of the minimal model programme do nothold over an algebraically closed field of characteristic two. Indeed, weconstruct a three dimensional plt pair whose codimension one part is notnormal, a three dimensional klt singularity which is not rational norCohen-Macaulay, and a klt Fano threefold with non-trivial intermediatecohomology.

JOURNAL ARTICLE

Cascini P, Tanaka H, 2018, Smooth rational surfaces violating Kawamata-Viehweg vanishing, EUROPEAN JOURNAL OF MATHEMATICS, Vol: 4, Pages: 162-176, ISSN: 2199-675X

JOURNAL ARTICLE

Cascini P, Tanaka H, Witaszek J, 2017, On log del Pezzo surfaces in large characteristic, COMPOSITIO MATHEMATICA, Vol: 153, Pages: 820-850, ISSN: 0010-437X

JOURNAL ARTICLE

Cascini P, Tasin L, On the Chern numbers of a smooth threefold, Transactions of the American Mathematical Society, ISSN: 0002-9947

We study the behaviour of Chern numbers of three dimensional terminalvarieties under divisorial contractions.

JOURNAL ARTICLE

Cascini P, Tanaka H, Witaszek J, 2017, Klt del Pezzo surfaces which are not Globally F-split, International Mathematics Research Notices, Pages: rnw300-rnw300, ISSN: 1073-7928

JOURNAL ARTICLE

Cascini P, Gongyo Y, Schwede K, 2016, UNIFORM BOUNDS FOR STRONGLY F-REGULAR SURFACES, TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, Vol: 368, Pages: 5547-5563, ISSN: 0002-9947

JOURNAL ARTICLE

Cascini P, McKernan J, Pereira JV, 2016, Foliation Theory in Algebraic Geometry, Publisher: Springer, ISBN: 9783319244600

Featuring a blend of original research papers and comprehensive surveys from an international team of leading researchers in the thriving fields of foliation theory, holomorphic foliations, and birational geometry, this book presents the ...

BOOK

Bisi C, Cascini P, Tasin L, 2016, A Remark on the Ueno-Campana's Threefold, MICHIGAN MATHEMATICAL JOURNAL, Vol: 65, Pages: 567-572, ISSN: 0026-2285

JOURNAL ARTICLE

Cascini P, Tanaka H, Xu C, 2015, ON BASE POINT FREENESS IN POSITIVE CHARACTERISTIC, ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE, Vol: 48, Pages: 1239-1272, ISSN: 0012-9593

JOURNAL ARTICLE

Cascini P, Hacon C, Mustata M, Schwede Ket al., 2014, ON THE NUMERICAL DIMENSION OF PSEUDO-EFFECTIVE DIVISORS IN POSITIVE CHARACTERISTIC, AMERICAN JOURNAL OF MATHEMATICS, Vol: 136, Pages: 1609-1628, ISSN: 0002-9327

JOURNAL ARTICLE

Cascini P, Lazic V, 2014, On the number of minimal models of a log smooth threefold, JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, Vol: 102, Pages: 597-616, ISSN: 0021-7824

JOURNAL ARTICLE

Cascini P, McKernan J, Mustata M, 2014, THE AUGMENTED BASE LOCUS IN POSITIVE CHARACTERISTIC, PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, Vol: 57, Pages: 79-87, ISSN: 0013-0915

JOURNAL ARTICLE

Cascini P, Nakamaye M, 2014, Seshadri constants on smooth threefolds, ADVANCES IN GEOMETRY, Vol: 14, Pages: 59-79, ISSN: 1615-715X

JOURNAL ARTICLE

Cascini P, Zhang D-Q, 2014, EFFECTIVE FINITE GENERATION FOR ADJOINT RINGS, ANNALES DE L INSTITUT FOURIER, Vol: 64, Pages: 127-144, ISSN: 0373-0956

JOURNAL ARTICLE

Cascini P, 2013, Rational Curves on Complex Manifolds, MILAN JOURNAL OF MATHEMATICS, Vol: 81, Pages: 291-315, ISSN: 1424-9286

JOURNAL ARTICLE

Cascini P, Panov D, 2012, SYMPLECTIC GENERIC COMPLEX STRUCTURES ON FOUR-MANIFOLDS WITH b(+)=1, JOURNAL OF SYMPLECTIC GEOMETRY, Vol: 10, Pages: 493-502, ISSN: 1527-5256

JOURNAL ARTICLE

Cascini P, Lazic V, 2012, NEW OUTLOOK ON THE MINIMAL MODEL PROGRAM, I, DUKE MATHEMATICAL JOURNAL, Vol: 161, Pages: 2415-2467, ISSN: 0012-7094

JOURNAL ARTICLE

Cascini P, Lazic V, 2012, The Minimal Model Program revisited, CONTRIBUTIONS TO ALGEBRAIC GEOMETRY: IMPANGA LECTURE NOTES, Pages: 169-+

JOURNAL ARTICLE

Birkar C, Cascini P, Hacon CD, McKernan Jet al., 2010, EXISTENCE OF MINIMAL MODELS FOR VARIETIES OF LOG GENERAL TYPE, JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, Vol: 23, Pages: 405-468, ISSN: 0894-0347

JOURNAL ARTICLE

FA Bogomolov, PCascini, B de Oliveira, 2006, Singularities on Complete Algebraic Varieties, Central European Journal of Math, Vol: 4, Pages: 194-208

We prove that any finite set of n-dimensional isolated algebraic singularities can be afforded on a simply connected projective variety.

JOURNAL ARTICLE

P Cascini, 2006, Subsheaves of the Cotangent Bundle, Central European Journal of Math., Vol: 4, Pages: 209-224

For any smooth projective variety, we study a birational invariant, deﬁned by Campana which depends on the Kodaira dimension of the subsheaves of the cotangent bundle of the variety and its exterior powers. We provide new bounds for a related invariant in any dimension and in particular we show that it is equal to the Kodaira dimension of the variety, in dimension up to 4, if this is not negative.

JOURNAL ARTICLE

Cascini P, Nave GL, 2005, Kähler-Ricci Flow and the Minimal Model Program for Projective Varieties

In this note we propose to show that the K\"ahler-Ricci flow fits naturallywithin the context of the Minimal Model Program for projective varieties. Inparticular we show that the flow detects, in finite time, the contractiontheorem of any extremal ray and we analyze the singularities of the metric inthe case of divisorial contractions for varieties of general type. In case onehas a smooth minimal model of general type (i.e., the canonical bundle is nefand big), we show infinite time existence and analyze the singularities.

JOURNAL ARTICLE

Cascini P, 2002, On the moduli space of the Schwarzenberger bundles, PACIFIC JOURNAL OF MATHEMATICS, Vol: 205, Pages: 311-323, ISSN: 0030-8730

JOURNAL ARTICLE

Cascini P, 2001, Weighted Tango bundles on IPn and their moduli spaces, FORUM MATHEMATICUM, Vol: 13, Pages: 251-260, ISSN: 0933-7741

JOURNAL ARTICLE

Cascini P, 1999, On a compactification of the moduli space of the rational normal curves

For any odd $n$, we describe a smooth minimal (i.e. obtained by adding anirreducible hypersurface) compactification $\tilde S_n$ of the quasi-projectivehomogeneous variety $S_{n}=PGL(n+1)/SL(2)$ that parameterizes the rationalnormal curves in $P^n$. We show that $\tilde S_{n}$ is isomorphic to acomponent of the Maruyama scheme of the semi-stable sheaves on $P^n$ of rank$n$ and Chern polynomial $(1+t)^{n+2}$ and we compute its Betti numbers. In particular $\tilde S_{3}$ is isomorphic to the variety of nets of quadricsdefining twisted cubics, studied by G. Ellinsgrud, R. Piene and S. Str{\o}mme(Space curves, Proc. Conf., LNM 1266).

WORKING PAPER

Cascini P, Gongyo Y, On the anti-canonical ring and varieties of Fano type

We study the anti-canonical ring of a projective variety and we characterisevarieties of log Fano type depending on the singularities of these models.

WORKING PAPER

Cascini P, Spicer C, MMP for co-rank one foliation on threefolds

We prove existence of flips, special termination, the base point free theoremand, in the case of log general type, the existence of minimal models for F-dltfoliated log pairs of co-rank one on a projective threefold. As applications, we show the existence of F-dlt modifications andF-terminalisations for foliated log pairs and we show that foliations withcanonical or F-dlt singularities admit non-dicritical singularities. Finally,we show abundance in the case of numerically trivial foliated log pairs.

JOURNAL ARTICLE

Cascini P, Meng S, Zhang D-Q, Polarized endomorphisms of normal projective threefolds in arbitrary characteristic

Let $X$ be a projective variety over an algebraically closed field $k$ ofarbitrary characteristic $p \ge 0$. A surjective endomorphism $f$ of $X$ is$q$-polarized if $f^\ast H \sim qH$ for some ample Cartier divisor $H$ andinteger $q > 1$. Suppose $f$ is separable and $X$ is $\mathbb{Q}$-Gorenstein and normal. Weshow that the anti-canonical divisor $-K_X$ is numerically equivalent to aneffective $\mathbb{Q}$-Cartier divisor, strengthening slightly the conclusionof Boucksom, de Fernex and Favre (Theorem C) and also covering singularvarieties over an algebraically closed field of arbitrary characteristic. Suppose $f$ is separable and $X$ is normal. We show that the Albanesemorphism of $X$ is an algebraic fibre space and $f$ induces polarizedendomorphisms on the Albanese and also the Picard variety of $X$, and $K_X$being pseudo-effective and $\mathbb{Q}$-Cartier means being a torsion$\mathbb{Q}$-divisor. Let $f^{Gal}:\overline{X}\to X$ be the Galois closure of $f$. We show that if$p>5$ and co-prime to $deg\, f^{Gal}$ then one can run the minimal modelprogram (MMP) $f$-equivariantly, after replacing $f$ by a positive power, for amildly singular threefold $X$ and reach a variety $Y$ with torsion canonicaldivisor (and also with $Y$ being a quasi-\'etale quotient of an abelian varietywhen $\dim(Y)\le 2$). Along the way, we show that a power of $f$ acts as ascalar multiplication on the Neron-Severi group of $X$ (modulo torsion) when$X$ is a smooth and rationally chain connected projective variety of dimensionat most three.

JOURNAL ARTICLE

Cascini P, Tanaka H, Relative semi-ampleness in positive characteristic

Given an invertible sheaf on a fibre space between projective varieties ofpositive characteristic, we show that fibrewise semi-ampleness implies relativesemi-ampleness. The same statement fails in characteristic zero.

JOURNAL ARTICLE

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