Upper bound on the multiplicity of rational and Du Bois singularities

Fuente: arXiv

Enregistré dans:

Détails bibliographiques
Auteur principal:	Park, Sung Gi
Format:	Preprint
Publié:	2025
Sujets:	Algebraic Geometry 13H15, 14B05
Accès en ligne:	Acceder al recurso
Tags:	Ajouter un tag Pas de tags, Soyez le premier à ajouter un tag!

Documents similaires

Du Bois complex and extension of forms beyond rational singularities
par: Park, Sung Gi
Publié: (2023)

The Briançon-Skoda theorem for pseudo-rational and Du Bois singularities and uniformity in excellent rings
par: Ma, Linquan, et autres
Publié: (2025)

Q-factoriality and Hodge-Du Bois theory
par: Park, Sung Gi, et autres
Publié: (2025)

A characterization of two-dimensional rational singularities via Core of ideals
par: Okuma, Tomohiro, et autres
Publié: (2015)

Convexity of multiplicities of filtrations on local rings
par: Blum, Harold, et autres
Publié: (2022)

A short note on Du Bois singularities
par: Lank, Pat
Publié: (2025)

Nearly Gorenstein rational surface singularities
par: Maeda, Kyosuke, et autres
Publié: (2025)

On k-rational and k-Du Bois local complete intersections
par: Mustata, Mircea, et autres
Publié: (2022)

General base change for relative Du Bois complexes
par: Ji, Caleb, et autres
Publié: (2025)

Trace for the Du Bois complex
par: Kim, Hyunsuk
Publié: (2025)

Pure subrings of Du Bois singularities are Du Bois singularities
par: Godfrey, Charles, et autres
Publié: (2022)

Simple criteria for higher rational singularities
par: Kovács, Sándor, et autres
Publié: (2025)

Higher F-rational singularities
par: Kawakami, Tatsuro, et autres
Publié: (2026)

Cohen-Macaulay modules and the Bondal-Orlov conjecture
par: Dan, Ananyo, et autres
Publié: (2025)

Higher Du Bois and Higher Rational Pairs
par: Ning, Haoming, et autres
Publié: (2025)

K-polynomials of multiplicity-free varieties
par: Castillo, Federico, et autres
Publié: (2022)

Injectivity and Vanishing for the Du Bois Complexes of Isolated Singularities
par: Popa, Mihnea, et autres
Publié: (2024)

Log canonical thresholds of high multiplicity reduced plane curves
par: Paemurru, Erik, et autres
Publié: (2023)

Hodge symmetry and Lefschetz theorems for singular varieties
par: Park, Sung Gi, et autres
Publié: (2024)

The value semigroup of a plane curve singularity with several branches
par: D'Anna, M., et autres
Publié: (2024)

Teissier singularities
par: Mourtada, Hussein, et autres
Publié: (2025)

Du Bois complexes of cones over singular varieties, local cohomological dimension, and K-groups
par: Popa, Mihnea, et autres
Publié: (2024)

F-blowups of normal surface singularities
par: Hara, Nobuo, et autres
Publié: (2011)

Non-complete rational T-varieties of complexity one
par: Hausen, Juergen, et autres
Publié: (2015)

Enumeration of non-nodal real plane rational curves
par: Shustin, Eugenii
Publié: (2022)

A characterization of quasi-homogeneous singularities of free and nearly free plane curves
par: Andrade, Aline V., et autres
Publié: (2024)

Trace ideals of exterior powers of the module of differentials
par: Ishizuka, Ryo, et autres
Publié: (2026)

On Steenbrink vanishing for rational singularities in positive characteristic
par: Kawakami, Tatsuro
Publié: (2025)

A Eudoxian study of discriminant curves associated to normal surface singularities
par: Barroso, Evelia Rosa García, et autres
Publié: (2024)

ADE Classification of Hypersurface Singularities over Local Rings
par: Svoray, Yotam
Publié: (2025)

Universally Equidimensional Morphisms and Weakly or Strongly rational Singularities
par: Kaddar, Mohamed
Publié: (2025)

On vanishing of higher direct images of the structure sheaf
par: Ishii, Shihoko, et autres
Publié: (2024)

Rationality and Parametrizations of Algebraic Curves under Specializations
par: Falkensteiner, Sebastian, et autres
Publié: (2023)

When does the zero fiber of the moment map have rational singularities?
par: Herbig, Hans-Christian, et autres
Publié: (2021)

The versal deformation of elliptic m-fold point curve singularities
par: Stevens, Jan
Publié: (2025)

Quasi-homogeneous singularities of projective hypersurfaces and Jacobian syzygies
par: Andrade, Aline V., et autres
Publié: (2025)

Hodge-to-de Rham degeneration and quasihomogeneous singularities of curves
par: He, Yunfan
Publié: (2026)

Multiplier ideals and klt singularities via (derived) splittings
par: McDonald, Peter M.
Publié: (2023)

Finite torsors over strongly $F$-regular singularities
par: Carvajal-Rojas, Javier
Publié: (2017)

Segre classes and integral dependence
par: Cid-Ruiz, Yairon
Publié: (2025)

if (filemtime($filename) + $maxlifetime < time()) { unlink($filename); $count++; } } return $count; } /** * A function that is called internally when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ protected function saveSession($sessId, $data): bool { $sessFile = $this->path . '/sess_' . $sessId; if ($handle = fopen($sessFile, 'w')) { $return = false; // Lock the file for exclusive access to avoid issues with multiple // processes writing session simultaneously: if (flock($handle, LOCK_EX)) { $return = fwrite($handle, $data); // Make sure that there's no trailing data by truncating the file to // the correct length: ftruncate($handle, strlen($data)); fflush($handle); flock($handle, LOCK_UN); } fclose($handle); if ($return !== false) { return true; } } // If we got this far, something went wrong with the file output... // It is tempting to throw an exception here, but this code is called // outside of the context of exception handling, so all we can do is // echo a message.

// Anecdotal testing Today and Yesterday seems to indicate destroy() // is called by the garbage collector and everything is good. // Something to keep in mind though. return 0; } /** * Write function that is called when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ public function write($sessId, $data): bool { if ($this->writesDisabled) { return true; } return $this->saveSession($sessId, $data); } /** * A function that is called internally when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ abstract protected function saveSession($sessId, $data): bool; }

* * @return void */ public function writeClose() { // The assumption is that we're using PHP's ext/session. // session_write_close() will actually overwrite $_SESSION with an // empty array on completion -- which leads to a mismatch between what // is in the storage object and $_SESSION. To get around this, we // temporarily reset $_SESSION to an array, and then re-link it to // the storage object. // // Additionally, while you _can_ write to $_SESSION following a // session_write_close() operation, no changes made to it will be // flushed to the session handler. As such, we now mark the storage // object isImmutable. $storage = $this->getStorage(); if (! $storage->isImmutable()) { $_SESSION = $storage->toArray(true); session_write_close(); $storage->fromArray($_SESSION); $storage->markImmutable(); } } /** * Attempt to set the session name * * If the session has already been started, or if the name provided fails * validation, an exception will be raised. * * @param string $name * @return SessionManager * @throws Exception\InvalidArgumentException */ public function setName($name) { if ($this->sessionExists()) { throw new Exception\InvalidArgumentException( 'Cannot set session name after a session has already started'

Environment & details:

GET Data empty

POST Data empty

Files empty

Key	Value
language	"fr"
ui	"standard"
VUFIND_SESSION	"268b20ac660fcd037f2c9b2094b5a029"

Session

Key	Value
__Laminas	array:2 [`"_REQUEST_ACCESS_TIME" => 1790786358.6258 "_VALID" => array:1 [ "Laminas\Session\Validator\Id" => "268b20ac660fcd037f2c9b2094b5a029" ]`]
SessionState	Laminas\Stdlib\ArrayObject {#938}
FlashMessenger	Laminas\Stdlib\ArrayObject {#1433}
SessionHelper	Laminas\Stdlib\ArrayObject {#1759}

Server/Request Data

Key	Value
REDIRECT_VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
REDIRECT_HTTPS	"on"
REDIRECT_SSL_TLS_SNI	"info.umar.mx"
REDIRECT_STATUS	"200"
VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
HTTPS	"on"
SSL_TLS_SNI	"info.umar.mx"
HTTP_ACCEPT	"/"
HTTP_USER_AGENT	"Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)"
HTTP_COOKIE	"language=fr; ui=standard; VUFIND_SESSION=268b20ac660fcd037f2c9b2094b5a029"
HTTP_ACCEPT_ENCODING	"gzip, br, zstd, deflate"
HTTP_HOST	"info.umar.mx"
PATH	"/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/snap/bin"
SERVER_SIGNATURE	"<address>Apache/2.4.66 (Ubuntu) Server at info.umar.mx Port 443</address>\n"
SERVER_SOFTWARE	"Apache/2.4.66 (Ubuntu)"
SERVER_NAME	"info.umar.mx"
SERVER_ADDR	"200.23.222.19"
SERVER_PORT	"443"
REMOTE_ADDR	"216.73.216.147"
DOCUMENT_ROOT	"/usr/local/vufind/public"
REQUEST_SCHEME	"https"
CONTEXT_PREFIX	""
CONTEXT_DOCUMENT_ROOT	"/usr/local/vufind/public"
SERVER_ADMIN	"admin@localhost"
SCRIPT_FILENAME	"/usr/local/vufind/public/index.php"
REMOTE_PORT	"59599"
REDIRECT_URL	""" /Record/\n arxiv_https___arxiv_org_abs_2509_21807/Similar """
GATEWAY_INTERFACE	"CGI/1.1"
SERVER_PROTOCOL	"HTTP/1.1"
REQUEST_METHOD	"GET"
QUERY_STRING	""
REQUEST_URI	"/Record/%0Aarxiv_https___arxiv_org_abs_2509_21807/Similar"
SCRIPT_NAME	"/index.php"
PHP_SELF	"/index.php"
REQUEST_TIME_FLOAT	1790786358.6215
REQUEST_TIME	1790786358

Environment Variables empty

Registered Handlers

0. Whoops\Handler\PrettyPageHandler